Marc Yor

Renewal series and square-root boundaries for Bessel processes (2008)

These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first...

Enriquez, Nathanael, Sabot, Christophe, Yor, Marc

We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical...

From Black-Scholes and Dupire formulae to last passage times of local martingales. Part A : The infinite time horizon (2008)

Three Notes on Connections between the Riemann Zeta Function and Probability Theory, in particular : Random Matrix Theory (Number Theory and Probability Theory) (2008)

These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first...

On the time to reach maximum for a variety of constrained Brownian motions (2008)

Majumdar, Satya. N., Randon-Furling, Julien, Kearney, Michael J., Yor, Marc

We derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit...

IMS Lecture Notes Monograph (2008)

THE TWO-PARAMETER POISSON–DIRICHLET DISTRIBUTION DERIVED FROM (2008)

Some properties of the arc-sine law related to its invariance under a family of rational maps ∗

A Stable Subordinator, Jim Pitman, Marc Yor

The two-parameter Poisson–Dirichlet distribution, denoted PD�α � θ�, is a probability distribution on the set of decreasing positive sequences with sum 1. The usual Poisson–Dirichlet...

This article appeared in Itô’s Stochastic Calculus and Probability (2008)

Jim Pitman, Marc Yor, Edited N. Ikeda, S. Watanabe, M. Fukushima

reprinted from the original tex source, August 3, 2004

On the time to reach maximum for a variety of constrained Brownian motions (2008)

Majumdar, Satya. N., Randon-Furling, Julien, Kearney, Michael J., Yor, Marc

We derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit...

On the time to reach maximum for a variety of constrained Brownian motions (2008)

Majumdar, Satya. N., Randon-Furling, Julien, Kearney, Michael J., Yor, Marc

We derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit...

An alternative expression for the Black-Scholes formula in terms of Brownian first and last passage times (2008)

An alternative expression for the Black-Scholes formula in terms of Brownian first and last passage times (2008)

The celebrated Black-Scholes formula which gives the price of a European option, may be expressed as the cumulative function of a last passage time of Brownian motion. A related result involving...

Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX (2008)

The celebrated Black-Scholes formula which gives the price of a European option, may be expressed as the cumulative function of a last passage time of Brownian motion. A related result involving...

A global view of Brownian penalisations (2008)

We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the case of the additive functional :...

Najnudel, J., Roynette, Bernard, Yor, Marc

pas de résumé

Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX (2008)

A global view of Brownian penalisations (2008)

We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the case of the additive functional :...

Najnudel, J., Roynette, Bernard, Yor, Marc

pas de résumé

From Black-Scholes formula, to local times and last passage times for certain submartingales (2008)

From Black-Scholes formula, to local times and last passage times for certain submartingales (2008)

Motivated by an expression of the standard Black-Scholes formula as (a multiple of) the cumulative function of a certain distribution on $\/Bbb R_+$, we discuss a general extension of this identity...

Ten penalisation results of Brownian motion involving its one-sided supremum until first and last passage times, VIII (2008)

Motivated by an expression of the standard Black-Scholes formula as (a multiple of) the cumulative function of a certain distribution on $\/Bbb R_+$, we discuss a general extension of this identity...

Penalisation of Brownian motion with its maximum and minimum processes as weak forms of Skorokhod embedding, X (2008)

We penalise Brownian motion by a function of its one-sided supremum considered up to the last zero before $t$, resp. first zero after $t$, of that Brownian motion. This study presents some analogy...

Ten penalisation results of Brownian motion involving its one-sided supremum until first and last passage times, VIII (2008)

We develop a Brownian penalisation procedure related to weight processes $(F_t$) of the type : $F_t := f(I_t, S_t) where $f$ is a bounded function with compact support and $S_t (resp. I_t)$ is the...

Penalisation of Brownian motion with its maximum and minimum processes as weak forms of Skorokhod embedding, X (2008)

We penalise Brownian motion by a function of its one-sided supremum considered up to the last zero before $t$, resp. first zero after $t$, of that Brownian motion. This study presents some analogy...

Unifying Black-Scholes type formulae which involve Brownian last passage times up to a finite horizon (2008)

We develop a Brownian penalisation procedure related to weight processes $(F_t$) of the type : $F_t := f(I_t, S_t) where $f$ is a bounded function with compact support and $S_t (resp. I_t)$ is the...

Unifying Black-Scholes type formulae which involve Brownian last passage times up to a finite horizon (2008)

The authors recently discovered some interesting relations between the Black-Scholes formula and last passage times of the Brownian exponential martingales, which invites one to seek analogous...

From Black-Scholes and Dupire formulae to last passage times of local martingales. Part A : The infinite time horizon (2008)

The authors recently discovered some interesting relations between the Black-Scholes formula and last passage times of the Brownian exponential martingales, which invites one to seek analogous...

From Black-Scholes and Dupire formulae to last passage times of local martingales. Part A : The infinite time horizon (2008)

These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first...

From Black-Scholes and Dupire formulae to last passage times of local martingales. Part B : The finite time horizon (2008)

These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first...

A family of generalized gamma convoluted variables (2008)

These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first...

Renewal series and square-root boundaries for Bessel processes (2008)

This paper consists of three parts: in the first part, we describe a family of generalized gamma convoluted (abbreviated as GGC) variables. In the second part, we use this description toprove that...

Enriquez, Nathanael, Sabot, Christophe, Yor, Marc

We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical...

From Black-Scholes and Dupire formulae to last passage times of local martingales. Part B : The finite time horizon (2008)

A family of generalized gamma convoluted variables (2008)

These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first...

Renewal series and square-root boundaries for Bessel processes (2008)

This paper consists of three parts: in the first part, we describe a family of generalized gamma convoluted (abbreviated as GGC) variables. In the second part, we use this description toprove that...

Enriquez, Nathanael, Sabot, Christophe, Yor, Marc

We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical...

Put option prices as joint distribution functions in strike and maturity : the Black-Scholes case (2008)

Put option prices as joint distribution functions in strike and maturity : the Black-Scholes case (2008)

For a large class of $\mathbb{R}_{+}$ valued, continuous local martingales $(M_{t}\; t \ge 0)$, with $M_{0} =1$ and $M_{\infty} = 0$, the put quantity : $\Pi_{M} (K,t) = E \big((K-M_{t})^{+} \big)$...

Existence and properties of pseudo-inverses for Bessel and related processes (2008)

For a large class of $\mathbb{R}_{+}$ valued, continuous local martingales $(M_{t}\; t \ge 0)$, with $M_{0} =1$ and $M_{\infty} = 0$, the put quantity : $\Pi_{M} (K,t) = E \big((K-M_{t})^{+} \big)$...

An interesting family of Black-Scholes perpetuities (2008)

It is shown that the tail probability of a Bessel process is the distributio function of a random time which is related to first and last passage times of Bessel processes

Existence and properties of pseudo-inverses for Bessel and related processes (2008)

We obtain the Laplace transform and integrability properties of the integral over $\Bbb R_+$ of the call quantity associated with geometric Brownian motion with negative drift, thus adding a new...

An interesting family of Black-Scholes perpetuities (2008)

It is shown that the tail probability of a Bessel process is the distributio function of a random time which is related to first and last passage times of Bessel processes

A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion. (2008)

We obtain the Laplace transform and integrability properties of the integral over $\Bbb R_+$ of the call quantity associated with geometric Brownian motion with negative drift, thus adding a new...

Baker, David, Yor, Marc

We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion. This provides a short proof of the recent result due to P. Carr et al [5] that the...

A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion. (2008)

Baker, David, Yor, Marc

We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion. This provides a short proof of the recent result due to P. Carr et al [5] that the...

motions motivated by models of insider trading 1 (2007)

Ching-tang Wu, Marc Yor

transformations of two independent Brownian

Path decompositions of a Brownian bridge related to the ratio of its maximum and amplitude (2007)

The joint law of the last zeros of Brownian motion and of its Lévy transform (2007)

We give two new proofs of Cs'aki's formula for the law of the ratio 1 \Gamma Q of the maximum relative to the amplitude (i.e. the maximum minus minimum) for a standard Brownian bridge. The...

3 (2007)

Hans Follmer, Ching-tang Wu, Marc Yor

We show the existence, for any k 2 N, of processes which have the same k-marginals as Brownian motion, although they are not Brownian motions. For k = 4, this proves a conjecture of Stoyanov. The law...

y (2007)

Jim Pitman, Marc Yor, Marie Curie

divisible laws associated with hyperbolic functions

Catherine Donati-Martin, Zhan Shi, Marc Yor

for a number of recent studies. As is well-known, in the particular case ¯ = 1, (B (1) t ; t 0), the L'evy transform of B, is a Brownian motion, and some interest in the pair (B; B (1) ) stems...

An explicit Skorokhod embedding for the age of (2007)

Paris Cnrs (umr, J. Obloj, M. Yor, Warszawa Poland, Marc Yor

Brownian excursions and Azéma martingale

Asset Prices are Brownian motion: Business Time.* (2007)

Only In, Helyette Geman, Dilip B. Madan, Marc Yor

This paper argues that asset price processes arising from market clearing conditions should be modeled as pure jump processes, with no continuous martingale component. However, we show that...

Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions (2007)

and the times spent by X above and below level y up to time (2007)

This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability...

motions motivated by models of insider trading 1 (2007)

Hitting, occupation, and inverse local times of one-dimensional diffusions: martingale and

3 (2007)

Hans Follmer, Ching-tang Wu, Marc Yor

We show the existence, for any k 2 N, of processes which have the same k-marginals as Brownian motion, although they are not Brownian motions. For k = 4, this proves a conjecture of Stoyanov. The law...

Hans Follmer, Ching-tang Wu, Marc Yor

transformations of two independent Brownian

Where Did The Brownian Particle Go? (2007)

Robin Pemantle, Yuval Peres, Jim Pitman, Marc Yor

Consider the radial projection onto the unit sphere of the path a d-dimensional Brownian motion W, started at the center of the sphere and run for unit time. Given the occupation measure of this...

by (2007)

invariance under a family (2007)

the relative lengths of excursions derived from a stable subordinator

Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions (2007)

properties of the arc sine law related to its

Where Did The Brownian Particle Go? (2007)

This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability...

Robin Pemantle Yuval, Yuval Peres, Jim Pitman, Marc Yor

Consider the radial projection onto the unit sphere of the path a d-dimensional Brownian motion W , started at the center of the sphere and run for unit time.

SOME MARTINGALES ASSOCIATED TO REFLECTED LÉVY PROCESSES (2007)

Paris Cnrs (umr, Laurent Nguyen-ngoc, Marc Yor

Some martingales associated to reflected Lévy processes L. NGUYEN-NGOC & M. YOR NOVEMBRE 2003

Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples (2007)

James, Lancelot F., Roynette, Bernard, Yor, Marc

In Section 1, we present a number of classical results concerning the Generalized Gamma Convolution (:GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet processes.To...

The barnes G function and its relations with sums and products of generalized Gamma convolution variables (2007)

Nikeghbali, Ashkan, Yor, Marc

We give a probabilistic interpretation for the Barnes G-function which appears in random matrix theory and in analytic number theory in the important moments conjecture due to Keating-Snaith for the...

Quasi-invariance properties of a class of subordinators (2007)

Von Renesse, Max-K., Yor, Marc, Zambotti, Lorenzo

We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of...

The characteristic polynomial of a random unitary matrix: a probabilistic approach (2007)

Bourgade, Paul, Hughes, Chris, Nikeghbali, Ashkan, Yor, Marc

In this paper, we propose a probabilistic approach to the study of the characteristic polynomial of a random unitary matrix. We recover the Mellin Fourier transform of such a random polynomial, first...

Burkholder's submartingales from a stochastic calculus perspective (2007)

Euler's formulae for ζ(2n) and products of Cauchy variables (2007)

We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in...

Bourgade, Paul; Laboratoire De Probabilités Et Modèles Aléatoires, Université Paris 6; Paulbourgade@gmail.com, Fujita, Takahiko; Graduate School Of Commerce And Management, Hitotsubashi University; Takahikofujita@mta.biglobe.ne.jp, Yor, Marc; Laboratoire De Probabilités Et Modèles Aléatoires, Université Paris 6; Deaproba@proba.jussieu.fr

We show how to recover Euler's formula for ζ(2n), as well as Lχ4(2n+1), for any integer n, from the knowledge of the density of the product of independent standard Cauchy variables.

Euler's formulae for ζ(2n) and products of Cauchy variables (2007)

Bourgade, Paul; Laboratoire De Probabilités Et Modèles Aléatoires, Université Paris 6; Paulbourgade@gmail.com, Fujita, Takahiko; Graduate School Of Commerce And Management, Hitotsubashi University; Takahikofujita@mta.biglobe.ne.jp, Yor, Marc; Laboratoire De Probabilités Et Modèles Aléatoires, Université Paris 6; Deaproba@proba.jussieu.fr

We show how to recover Euler's formula for ζ(2n), as well as Lχ4(2n+1), for any integer n, from the knowledge of the density of the product of independent standard Cauchy variables.

Tilted stable subordinators, Gamma time changes and Occupation Time of rays by Bessel Spiders (2007)

James, Lancelot F., Yor, Marc

We exhibit, in the form of some identities in law, some connections between tilted stable subordinators, time-changed by independent Gamma processes and the occupation times of Bessel spiders, or...

Euler's formula for zeta(2n) and Cauchy variables (2007)

Bourgade, Paul, Fujita, Takahiko, Yor, Marc

Euler's formulae for zeta(2n) are recovered from the computation in two dierent manners of the even moments of log(|C1C2|), for C1 and C2 two independent standard Cauchy variables. The method...

Two examples of functional penalisations of Brownian motion, VIII (2007)

Penalizing a BES(d) process (0 < d < 2) with a function of its local time, V (2007)

On one hand, we penalise Brownian paths by a function of one-sided supremum of Brownian motion, considered up to the last, resp. the first, zero, before $t$, resp. after $t$. This study provides some...

Some extensions of Pitman's and Ray-Knight's theorems for penalized Brownian motions and their local times, IV (2007)

We study the penalization of a BES(d) process (0

Donati-Martin, Catherine, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We give some extensions of Pitman's and Ray-Knight's theorems via a penalization procedure involving Brownian motion and its local time at 0

We precise the choice of constants in computations related to Bessel processes with dimension d=2(1-alpha), 0 < alpha < 1

Burkholder's submartingales from a stochastic calculus perspective (2007)

Quasi-invariance properties of a class of subordinators (2007)

We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in...

Von Renesse, Max-K., Yor, Marc, Zambotti, Lorenzo

We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of...

Generalized Gamma convolutions, Dirichlet means, Thorin measures with explicit examples (2007)

James, L.F., Roynette, Bernard, Yor, Marc

In section 1, we present a number of classical results concerning the generalized Gamma convolution ( : GGC) variables, their Wiener-Gamma representations, and relation with Dirichlet processes. To a...

Generalized Gamma convolutions, Dirichlet means, Thorin measures with explicit examples (2007)

James, L.F., Roynette, Bernard, Yor, Marc

In section 1, we present a number of classical results concerning the generalized Gamma convolution ( : GGC) variables, their Wiener-Gamma representations, and relation with Dirichlet processes. To a...

Quasi-invariance properties of a class of subordinators (2007)

Von Renesse, Max-K., Yor, Marc, Zambotti, Lorenzo

We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of...

Burkholder's submartingales from a stochastic calculus perspective (2007)

Donati-Martin, Catherine, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in...

We precise the choice of constants in computations related to Bessel processes with dimension d=2(1-alpha), 0 < alpha < 1

Penalizing a BES(d) process (0 < d < 2) with a function of its local time, V (2007)

Some extensions of Pitman's and Ray-Knight's theorems for penalized Brownian motions and their local times, IV (2007)

We study the penalization of a BES(d) process (0

Two examples of functional penalisations of Brownian motion, VIII (2007)

We give some extensions of Pitman's and Ray-Knight's theorems via a penalization procedure involving Brownian motion and its local time at 0

Euler's formula for zeta(2n) and Cauchy variables (2007)

On one hand, we penalise Brownian paths by a function of one-sided supremum of Brownian motion, considered up to the last, resp. the first, zero, before $t$, resp. after $t$. This study provides some...

Bourgade, Paul, Fujita, Takahiko, Yor, Marc

Euler's formulae for zeta(2n) are recovered from the computation in two dierent manners of the even moments of log(|C1C2|), for C1 and C2 two independent standard Cauchy variables. The method...

On the excursion theory for linear diffusions (2006)

Salminen, Paavo, Vallois, Pierre, Yor, Marc

We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting...

Arcsine Laws and Interval Partitions Derived from a Stable Subordinator (2006)

On a particular class of self-decomposable random variables : the durations of Bessel excursions straddling independent exponential times. (2006)

Lévy discovered that the fraction of time a standard one-dimensional Brownian motion B spends positive before time t has arcsine distribution, both for t a fixed time when Bt ≠ 0 almost surely,...

Bertoin, J., Fujita, T., Roynette, Bernard, Yor, Marc

The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Althrough our study may be considered as a particular...

On a particular class of self-decomposable random variables : the durations of Bessel excursions straddling independent exponential times. (2006)

Bertoin, J., Fujita, T., Roynette, Bernard, Yor, Marc

The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Althrough our study may be considered as a particular...

A chaotic representation property of the multidimensional Dunkl processes (2006)

Gallardo, Léonard, Yor, Marc

Dunkl processes are martingales as well as c\`{a}dl\`{a}g homogeneous Markov processes taking values in $\mathbb{R}^d$ and they are naturally associated with a root system. In this paper we study the...

A chaotic representation property of the multidimensional Dunkl processes (2006)

Gallardo, Léonard, Yor, Marc

Dunkl processes are martingales as well as càdlàg homogeneous Markov processes taking values in ℝd and they are naturally associated with a root system. In this paper we study the jumps of these...

Linear transformations of two independent Brownian motions and orthogonal decompositions of Brownian filtrations (2006)

Wu, Ching-Tang, Yor, Marc

Brownian motions defined as linear transformations of two independent Brownian motions are studied, together with certain orthogonal decompositions of Brownian filtrations.

Asymptotic laws for compositions derived from transformed subordinators (2006)

Gnedin, Alexander, Pitman, Jim, Yor, Marc

A random composition of n appears when the points of a random closed set ℛ̃⊂[0,1] are used to separate into blocks n points sampled from the uniform distribution. We study the number of parts Kn...

CGMY and Meixner Subordinators are Absolutely Continuous with respect to One Sided Stable Subordinators. (2006)

CGMY and Meixner Subordinators are Absolutely Continuous with respect to One Sided Stable Subordinators. (2006)

We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable $(Y/2)$ subordinator while the...

CGMY and Meixner Subordinators are Absolutely Continuous with respect to One Sided Stable Subordinators (2006)

We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable $(Y/2)$ subordinator while the...

Random times and enlargements of filtrations in a Brownian setting / Roger Mansuy, Marc Yor (2006)

We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable $(Y/2)$ subordinator while the...

Mansuy, Roger, Yor, Marc

Incluye bibliografía e índice

On a particular class of self-decomposable random variables : the durations of Bessel excursions straddling independent exponential times. (2006)

Bertoin, J., Fujita, T., Roynette, Bernard, Yor, Marc

The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Althrough our study may be considered as a particular...

CGMY and Meixner Subordinators are Absolutely Continuous with respect to One Sided Stable Subordinators. (2006)

Limiting laws associated with Brownian motion perturbed by its maximum, minimum and local time II (2006)

We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable $(Y/2)$ subordinator while the...

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I. (2006)

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...

In memoriam : Paul-Andre Meyer : Séminaire de probabilités XXXIX / M. Émery, M. Yor (Eds.) (2006)

We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...

Meyer, Paul André, Yor, Marc

Incluye bibliografía e índice

Random Matrices and the Riemann zeta function (2006)

Bourgade, Paul, Yor, Marc

These notes are based on a talk given at the Institut de Mathématiques Elie Cartan de Nancy in June 2006. Their purpose is to introduce the reader to some links between two fields of mathematics :...

Some Explicit Krein Representations of Certain Subordinators, Including the Gamma Process (2006)

On the excursion theory for linear diffusions (2006)

We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have...

Salminen, Paavo, Vallois, Pierre, Yor, Marc

We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting...

Limiting laws associated with Brownian motion perturbed by its maximum, minimum and local time II (2006)

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I. (2006)

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...

On the excursion theory for linear diffusions (2006)

We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...

Salminen, Paavo, Vallois, Pierre, Yor, Marc

We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting...

Random Matrices and the Riemann zeta function (2006)

Bourgade, Paul, Yor, Marc

These notes are based on a talk given at the Institut de Mathématiques Elie Cartan de Nancy in June 2006. Their purpose is to introduce the reader to some links between two fields of mathematics :...

On a particular class of self-decomposable random variables : the durations of Bessel excursions straddling independent exponential times. (2006)

Bertoin, J., Fujita, T., Roynette, Bernard, Yor, Marc

The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Althrough our study may be considered as a particular...

CGMY and Meixner Subordinators are Absolutely Continuous with respect to One Sided Stable Subordinators. (2006)

Exponential functionals of Brownian motion, I: Probability laws at fixed time (2005)

We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable $(Y/2)$ subordinator while the...

Exponential functionals of Brownian motion, II: Some related diffusion processes (2005)

This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several...

A note on a.s. finiteness of perpetual integral functionals of diffusions (2005)

This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have...

A note on a.s. finiteness of perpetual integral functionals of diffusions (2005)

In this note, with the help of the boundary classification of diffusions, we derive a criterion of the convergence of perpetual integral functionals of transient real-valued diffusions. In the...

A note on a.s. finiteness of perpetual integral functionals of diffusions (2005)

In this note, with the help of the boundary classification of diffusions, we derive a criterion of the convergence of perpetual integral functionals of transient real-valued diffusions. In the...

Exponential functionals of Levy processes (2005)

In this note, with the help of the boundary classification of diffusions, we derive a criterion of the convergence of perpetual integral functionals of transient real-valued diffusions. In the...

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2005)

This text surveys properties and applications of the exponential functional $\int_0^t\exp(-\xi_s)ds$ of real-valued L\'evy processes $\xi=(\xi_t,t\geq0)$.

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2005)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2005)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum

Limiting laws associated with Brownian motion perturbed by its maximum, minmum and local time II (2005)

Results of penalization of a one-dimensional Brownian motion $(X_t) $, by its one-sided maximum $\dis (S_t=\sup_{0 \leq u \leq t}X_u)$, which were recently obtained by the authors are improved with...

Limiting laws associated with Brownian motion perturbed by its maximum, minmum and local time II (2005)

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I (2005)

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...

Limiting laws associated with Brownian motion perturbed by its maximum, minmum and local time II (2005)

We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I. (2005)

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...

Limiting laws associated with Brownian motion perturbated by normalized exponential weights I. (2005)

We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...

Options on Hedge Funds under the High Water Mark Rule (2005)

We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...

Options on Hedge Funds under the High Water Mark Rule (2005)

The rapidly growing hedge fund industry has provided individual and institutional investors with new investment vehicles and styles of management. It has also brought forward a new form of...

Options on Hedge Funds under the High Water Mark Rule (2005)

The rapidly growing hedge fund industry has provided individual and institutional investors with new investment vehicles and styles of management. It has also brought forward a new form of...

Further examples of explicit Krein representations of certain subordinators (2005)

The rapidly growing hedge fund industry has provided individual and institutional investors with new investment vehicles and styles of management. It has also brought forward a new form of...

Further examples of explicit Krein representations of certain subordinators (2005)

In a previous paper , we have shown that the gamma subordinators may be represented as inverse local times of certain diffusions. In the present paper, we give such representations for other...

Further examples of explicit Krein representations of certain subordinators (2005)

In a previous paper , we have shown that the gamma subordinators may be represented as inverse local times of certain diffusions. In the present paper, we give such representations for other...

A definition and some characteristic properties of pseudo-stopping times (2005)

In a previous paper, we have shown that the gamma subordinators may be represented as inverse local times of certain diffusions. In the present paper, we give such representations for other...

Nikeghbali, Ashkan, Yor, Marc

Recently, Williams [Bull. London Math. Soc. 34 (2002) 610–612] gave an explicit example of a random time ρ associated with Brownian motion such that ρ is not a stopping time but...

Equivalent and absolutely continuous measure changes for jump-diffusion processes (2005)

Cheridito, Patrick, Filipovic, Damir, Yor, Marc

We provide explicit sufficient conditions for absolute continuity and equivalence between the distributions of two jump-diffusion processes that can explode and be killed by a potential.

Equivalent and absolutely continuous measure changes for jump-diffusion processes (2005)

Cheridito, Patrick, Filipović, Damir, Yor, Marc

We provide explicit sufficient conditions for absolute continuity and equivalence between the distributions of two jump-diffusion processes that can explode and be killed by a potential.

Perpetual Integral Functionals as Hitting and Occupation Times (2005)

Salminen, Paavo; Abo Akademi, Finland; Phsalmin@abo.fi, Yor, Marc; Université Pierre Et Marie Curie; Pitman@stat.berkeley.edu

Abstract. Let $X$ be a linear diffusion and $f$ a non-negative, Borel measurable function. We are interested in finding conditions on $X$ and $f$ which imply that the perpetual integral functional $$...

Wiener integrals for centered powers of Bessel processes, I (2005)

Funaki, Tadahisa, Hariya, Yuu, Yor, Marc, 舟木, 直久, 針谷, 祐, ヨー, マーク

Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality

Some explicit Krein representations of certain subordinators, including the Gamma process (2005)

Some explicit Krein representations of certain subordinators, including the Gamma process (2005)

We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have...

Some explicit Krein representations of certain subordinators, including the Gamma process (2005)

We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have...

"Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections" (2005)

We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have...

"Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections" (2005)

We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated...

Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections (2005)

We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated...

Exponential functionals of Brownian motion and disordered systems (2005)

We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated...

Comtet, Alain, Monthus, Cecile, Yor, Marc

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts such as continuous time finance models and one-dimensional disordered models. We study...

Starting from the potential theoretic definition of the local times of a Markov process - when these exist - we obtain a Tanaka formula for the local times of symmetric Lévy processes. The most...

Tanaka formula for symmetric L\'{e}vy processes (2005)

Starting from the potential theoretic definition of the local times of a Markov process - when these exist - we obtain a Tanaka formula for the local times of symmetric Lévy processes. The most...

Exponential functionals of Lévy processes (2005)

Starting from the potential theoretic definition of the local times of a Markov process - when these exist - we obtain a Tanaka formula for the local times of symmetric L\'{e}vy processes. The most...

Exponential functionals of Brownian motion, I: Probability laws at fixed time (2005)

This text surveys properties and applications of the exponential functional ∫0texp(−ξs)ds of real-valued Lévy processes ξ=(ξt,t≥0).

Exponential functionals of Brownian motion, II: Some related diffusion processes (2005)

This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several...

A definition and some characteristic properties of pseudo-stopping times (2005)

This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have...

Nikeghbali, A., Yor, Marc

Séminaire de probabilités XXXVIII / M. Émery, M. Ledoux, M. Yor (eds.) (2005)

Emery, M. (Michel), Yor, Marc

Incluye bibliografía e índice

A note on a.s. finiteness of perpetual integral functionals of diffusions (2005)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2005)

In this note, with the help of the boundary classification of diffusions, we derive a criterion of the convergence of perpetual integral functionals of transient real-valued diffusions. In the...

Options on Hedge Funds under the High Water Mark Rule (2005)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum

Further examples of explicit Krein representations of certain subordinators (2005)

The rapidly growing hedge fund industry has provided individual and institutional investors with new investment vehicles and styles of management. It has also brought forward a new form of...

Some explicit Krein representations of certain subordinators, including the Gamma process (2005)

In a previous paper , we have shown that the gamma subordinators may be represented as inverse local times of certain diffusions. In the present paper, we give such representations for other...

"Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections" (2005)

We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have...

We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated...

Couples de Wald indéfiniment divisibles. Exemples liés à la fonction gamma d'Euler et à la fonction zeta de Riemann (2005)

Starting from the potential theoretic definition of the local times of a Markov process - when these exist - we obtain a Tanaka formula for the local times of symmetric Lévy processes. The most...

Properties of perpetual integral functionals of brownian motion with drift (2005)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2005)

Options on Hedge Funds under the High Water Mark Rule (2005)

Limiting laws for long Brownian Bridges perturbed by their one-sided maximum

A note on a.s. finiteness of perpetual integral functionals of diffusions (2005)

The rapidly growing hedge fund industry has provided individual and institutional investors with new investment vehicles and styles of management. It has also brought forward a new form of...

Further examples of explicit Krein representations of certain subordinators (2005)

In this note, with the help of the boundary classification of diffusions, we derive a criterion of the convergence of perpetual integral functionals of transient real-valued diffusions. In the...

Some explicit Krein representations of certain subordinators, including the Gamma process (2005)

In a previous paper , we have shown that the gamma subordinators may be represented as inverse local times of certain diffusions. In the present paper, we give such representations for other...

"Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections" (2005)

We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have...

We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated...

Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions (2004)

Starting from the potential theoretic definition of the local times of a Markov process - when these exist - we obtain a Tanaka formula for the local times of symmetric Lévy processes. The most...

Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions (2004)

We describe some connections, via composition, between two functional spaces: the space of (sub)critical branching mechanisms and the space of Bernstein functions. The functions ${\bf e}_\alpha: x\to...

Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions (2004)

We describe some connections, via composition, between two functional spaces: the space of (sub)critical branching mechanisms and the space of Bernstein functions. The functions ${\bf e}_\alpha: x\to...

We describe some connections, via composition, between two functional spaces: the space of (sub)critical branching mechanisms and the space of Bernstein functions. The functions ${\bf e}_\alpha: x\to...

This text surveys properties and applications of the exponential functional $\int_{0}^{t}\exp(-\xi_s)ds$ of real-valued L\'evy processes $\xi=(\xi_t, t\geq0)$.

On local martingale and its supremum: harmonic functions and beyond (2004)

This text surveys properties and applications of the exponential functional $\int_{0}^{t}\exp(-\xi_s)ds$ of real-valued L\'evy processes $\xi=(\xi_t, t\geq0)$.

On local martingale and its supremum: harmonic functions and beyond (2004)

We discuss certain facts involving a continuous local martingale $N$ and its supremum $\overline{N}$. A complete characterization of $(N,\overline{N})$-harmonic functions is proposed. This yields an...

On local martingale and its supremum: harmonic functions and beyond (2004)

We discuss certain facts involving a continuous local martingale $N$ and its supremum $\overline{N}$. A complete characterization of $(N,\overline{N})$-harmonic functions is proposed. This yields an...

Harnesses, Levy bridges and Monsieur Jourdain (2004)

We discuss certain facts involving a continuous local martingale $N$ and its supremum $\bar{N}$. A complete characterization of $(N,\bar{N})$-harmonic functions is proposed. This yields an important...

Mansuy, Roger, Yor, Marc

Relations between so-called harness processes and initial enlargements of the filtration of a Levy process with its positions at fixed times are investigated.

A definition and some characteristic properties of pseudo-stopping times (2004)

Nikeghbali, Ashkan, Yor, Marc

Recently, D. Williams \cite{williams} gave an explicit example of a random time $\rho $ associated with Brownian motion such that $\rho $ is not a stopping time but...

Where did the Brownian particle go? (2004)

Pemantle, Robin, Peres, Yuval, Pitman, Jim, Yor, Marc

Consider the radial projection onto the unit sphere of the path a d-dimensional Brownian motion W, started at the center of the sphere and run for unit time. Given the occupation measure mu of this...

Asymptotic laws for compositions derived from transformed subordinators (2004)

Gnedin, Alexander, Pitman, Jim, Yor, Marc

A random composition of $n$ appears when the points of a random closed set $\widetilde{\mathcal{R}}\subset[0,1]$ are used to separate into blocks $n$ points sampled from the uniform distribution. We...

Perpetual integral functionals as hitting and occupation times (2004)

Some properties of the Wishart processes and a matrix extension of the Hartman-Watson laws (2004)

Let $X$ be a linear diffusion and $f$ a non-negative, Borel measurable function. We are interested in finding conditions on $X$ and $f$ which imply that the perpetual integral functional $$...

Donati-Martin, Catherine, Doumerc, Yan, Matsumoto, Hiroyuki, Yor, Marc

The aim of this paper is to discuss for Wishart processes some properties which are analogues of the corresponding well-known ones for Bessel processes. In fact, we mainly concentrate on the local...

A parallel between Brownian bridges and gamma bridges (2004)

Yor, Marc, Émery, Michel

Some properties of the Gamma bridges (obtained by conditioning the Gamma subordinator to take a given value at a given time) are investigated; similarities with the Brownian bridges are emphasized.

Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions (2004)

We describe some connections, via composition, between two functional spaces: the space of (sub)critical branching mechanisms and the space of Bernstein functions. The functions ${\bf e}_\alpha: x\to...

On local martingale and its supremum: harmonic functions and beyond (2004)

This text surveys properties and applications of the exponential functional $\int_{0}^{t}\exp(-\xi_s)ds$ of real-valued L\'evy processes $\xi=(\xi_t, t\geq0)$.

A trivariate law for certain processes related to perturbed brownian motions (2004)

We discuss certain facts involving a continuous local martingale $N$ and its supremum $\overline{N}$. A complete characterization of $(N,\overline{N})$-harmonic functions is proposed. This yields an...

Carmona, Philippe, Petit, Frédérique, Yor, Marc

Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions (2004)

We describe some connections, via composition, between two functional spaces: the space of (sub)critical branching mechanisms and the space of Bernstein functions. The functions ${\bf e}_\alpha: x\to...

On local martingale and its supremum: harmonic functions and beyond (2004)

This text surveys properties and applications of the exponential functional $\int_{0}^{t}\exp(-\xi_s)ds$ of real-valued L\'evy processes $\xi=(\xi_t, t\geq0)$.

Universit¶e Paris-Dauphine and ESSEC (2004)

We discuss certain facts involving a continuous local martingale $N$ and its supremum $\overline{N}$. A complete characterization of $(N,\overline{N})$-harmonic functions is proposed. This yields an...

Peter Carr, Dilip B. Madan, Marc Yor

We de¯ne the class of local L¶evy processes. These are L¶evy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the...

A survey and some generalizations of Bessel processes (2003)

Göing-Jaeschke, Anja, Yor, Marc

Bessel processes play an important role in financial mathematics because of their strong relation to financial models such as geometric Brownian motion or Cox-Ingersoll-Ross processes. We are...

On Dufresne's relation between the probability laws of exponential functionals of Brownian motions with different drifts (2003)

Hitting, occupation and inverse local times of one-dimensional diffusions: martingale and excursion approaches (2003)

Denote by αt(μ) the probability law of At(μ) = ∫0texp(2(Bs+μ s))ds for a Brownian motion {Bs, s ≥ 0}. It is well known that αt(μ) is of interest in a number of domains, e.g. mathematical...

A survey and some generalizations of Bessel processes (2003)

Basic relations between the distributions of hitting, occupation and inverse local times of a one-dimensional diffusion process $X$, first discussed by It\^o and McKean, are reviewed from the...

Anja Göing-jaeschke, Marc Yor

Bessel processes play an important role in financial mathematics because of their strong relation to financial processes like geometric Brownian motion or CIR processes. We are interested in the...

Making Markov martingales meet marginals: with explicit constructions (2002)

Madan, Dilip B., Yor, Marc

We present three generic constructions of martingales that all have the Markov property with known and prespecified marginal densities. These constructions are further invest\-igated for the special...

The fine structure of asset returns: an empirical investigation (2002)

Carr, Peter, Geman, Hélyette, Madan, Dilip B., Yor, Marc

We investigate the importance of diffusion and jumps in a new model for asset returns. In contrast to standard models, we allow for jump components displaying finite or infinite activity and...

The fine structure of asset returns: an empirical investigation (2002)

Carr, Peter, Geman, HÃ©lyette, Madan, Dilip B., Yor, Marc

We investigate the importance of diffusion and jumps in a new model for asset returns. In contrast to standard models, we allow for jump components displaying finite or infinite activity and...

The fine structure of asset returns: an empirical investigation (2002)

Carr, Peter, Geman, Hélyette, Madan, Dilip B., Yor, Marc

We investigate the importance of diffusion and jumps in a new model for asset returns. In contrast to standard models, we allow for jump components displaying finite or infinite activity and...

The fine structure of asset returns: an empirical investigation (2002)

Carr, Peter, Geman, Hélyette, Madan, Dilip B., Yor, Marc

We investigate the importance of diffusion and jumps in a new model for asset returns. In contrast to standard models, we allow for jump components displaying finite or infinite activity and...

On independent times and positions for Brownian motions (2002)

De Meyer, Bernard, Roynette, Bernard, Vallois, Pierre, Yor, Marc

Let $(B_t ; t \ge 0)$, $\big(\mbox{resp. }((X_t, Y_t) ; t \ge 0)\big)$ be a one (resp. two) dimensional Brownian motion started at 0. Let $T$ be a stopping time such that $(B_{t \wedge T} ; t \ge 0)$...

On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes (2002)

Séminaire de probabilités 1967-1980 : a selection in Martingale theory / Michel Emery, Marc Yor (eds.) (2002)

Séminaire De Probabilités, Yor, Marc

Articles reprinted from the first fourteen Séminaires de Probabilités

On independent times and positions for Brownian motions (2002)

Roynette, Bernard, Yor, Marc, Vallois, Pierre, Meyer, B. De

Linear transformations of two independent Brownian motions and orthogonal decompositions of Brownian filtrations (2002)

Wu, Ching-Tang, Yor, Marc

Brownian motions defined as linear transformations of two independent Brownian motions are studied, together with certain orthogonal decompositions of Brownian filtrations

On Subordinators, Self-Similar Markov Processes and Some Factorizations of the Exponential Variable (2001)

Bertoin, Jean; Universite Pierre Et Marie Curie; Jbe@ccr.jussieu.fr, Yor, Marc; Universite Pierre Et Marie Curie; Neil.O.connell@ens.fr

Let $xi$ be a subordinator with Laplace exponent $Phi$, $I=int_{0}^{infty}exp(-xi_s)ds$ the so-called exponential functional, and $X$ (respectively, $hat X$) the self-similar Markov process obtained...

A Representation for Non-Colliding Random Walks (2001)

O'Connell, Neil; BRIMS, HP Labs; Neil.O.connell@ens.fr, Yor, Marc; Universite Pierre Et Marie Curie; Neil.O.connell@ens.fr

We define a sequence of mappings $Gamma_k:D_0(R_+)^kto D_0(R_+)^k$ and prove the following result: Let $N_1,ldots,N_n$ be the counting functions of independent Poisson processes on $R_+$ with...

A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration (2001)

Large deviations for the Bessel clock (2001)

Yor, Marc, Zani, Marguerite

We show the law of large numbers, the central limit theorem and the large-deviation principle for the Bessel clock ∈t0t\rm d}s/(Rs(ν))2, where (Rt(ν), t≥0) is a Bessel process of index ν>0. We...

On the distribution of ranked heights of excursions of a Brownian bridge (2001)

Where Did the Brownian Particle Go? (2001)

The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge $(B^{br}_t, 0 \le t \le 1)$ is described. The height $M^{br +}_j$of the...

Pemantle, Robin; Ohio State University; Pemantle@math.ohio_state.edu, Peres, Yuval; University Of California, Berkeley; Peres@stat.berkeley.edu, Pitman, Jim; University Of California, Berkeley; Pitman@stat.berkeley.edu, Yor, Marc; Université Pierre Et Marie Curie; Pitman@stat.berkeley.edu

Consider the radial projection onto the unit sphere of the path a $d$-dimensional Brownian motion $W$, started at the center of the sphere and run for unit time. Given the occupation measure $mu$ of...

An analogue of Pitman's {$2M-X$} theorem for exponential Wiener functionals. II. The role of the generalized inverse Gaussian laws (2001)

Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions (2001)

In Part I of this work, we have shown that the stochastic process $Z^{(\mu)}$ defined by (8.1) below is a diffusion process, which may be considered as an extension of Pitman's $2M-X$ theorem. In...

Donati-Martin, Catherine, Matsumoto, Hiroyuki, Yor, Marc

We present some absolute continuity relationships between the probability laws of a geometric Brownian motion $e^{(\mu)}=\{e_t^{(\mu)},t\geqq0\}$ and its images by certain transforms $T_\alpha$...

Some consequences of the cyclic exchangeability property for exponential functionals of Lévy processes (2001)

Chaumont, Loïc, Hobson, David G., Yor, Marc

On certain Markov processes attached to exponential functionals of Brownian motion: application to Asian options. (2001)

Yor, Marc, Ghomrasni, R., Donati-Martin, C.

We obtain a closed formula for the Laplace transform of the first moment of certain exponential functionals of Brownian motion with drift, which gives the price of Asian options. The proof relies on...

Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities (2001)

Casadio Tarabusi, Enrico, Figà Talamanca, Alessandro, Yor, Marc, Baldi, Paolo

We study the law of functionals whose prototype is ?0+8 eBs(?) dWs(µ), where B(?) and W(µ) are independent Brownian motions with drift. These functionals appear naturally in risk theory as well as...

Term structures of credit spreads with incomplete accounting information (2001)

Darrell Duffie, David L, Martin Jacobsen, Marliese Uhrig-homburg, Marc Yor, Josef Zechner, ...

Abstract: We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer’s assets directly,...

Banc of America Securities (2001)

Peter Carr, Dilip B. Madan, Marc Yor

Three processes re°ecting persistence of volatility are formulated by evaluating three L¶evy processes at a time change given by the integral of a square root process. A positive stock price...

Stochastic Volatility for Lévy Processes (2001)

Peter Carr, Hélyette Geman, Dilip B. Madan, Marc Yor

Three processes reecting persistence of volatility are formulated by evaluating three Levy processes at a time change given by the integral of a square root process. A positive stock price process is...

Some measure-valued Markov processes attached to occupation times of Brownian motion (2000)

An analogue of Pitman's {$2M-X$} theorem for exponential Wiener functionals. I. A time-inversion approach (2000)

We study the positive random measure $\Pi_t (\omega, \d y) = l_t^{B_t -y}\d y$ , where $(l^a_t; a \in \R, t > 0)$ denotes the family of local times of the one-dimensional Brownian motion B. We prove...

Some invariance properties (of the laws) of Ocone's martingales (2000)

Let $\{B_t^{(\mu)},t\geqq0\}$ be a one-dimensional Brownian motion with constant drift $\mu\in{\bf R}$ starting from $0$. In this paper we show that $$ Z_t^{(\mu)} = \exp(-B_t^{(\mu)}) \int_0^t...

Vostrikova, Lioudmilla, Yor, Marc

On weak brownian motions of arbitrary order (2000)

The Fine Structure of Asset Returns: An Empirical Investigation (2000)

Peter Carr, Hélyette Geman, Dilip B. Madan, Marc Yor

We investigate the relative importance of diffusion and jumps in a new jump diffusion model for asset returns. In contrast to the standard modelling of jumps for asset returns, the jump component of...

Time Changes Hidden In Brownian Subordination (2000)

Helyette Geman, Dilip B. Madan, Marc Yor

We consider Brownian motion evaluated at a time change given by an independent purely discontinuous subordinator and inquire into the relation between the quadratic variation of the process and the...

Some asymptotic properties of the local time of the uniform empirical process (1999)

Csörgö, Miklós, Shi, Zhan, Yor, Marc

We study the almost sure asymptotic properties of the local time of the uniform empirical process. In particular, we obtain two versions of the law of the iterated logarithm for the integral of the...

Some Changes of Probabilities Related to a Geometric Brownian Motion Version of Pitman's 2M-X Theorem (1999)

Matsumoto, Hiroyuki; Nagoya University; Matsu@info.human.nagoya-u.ac.jp, Yor, Marc; Universite Pierre Et Marie Curie; Neil.O.connell@ens.fr

Rogers-Pitman have shown that the sum of the absolute value of $B^{(mu)}$, Brownian motion with constant drift $mu$, and its local time $L^{(mu)}$ is a diffusion $R^{(mu)}$. We exploit the...

The Law of the Maximum of a Bessel Bridge (1999)

Pitman, Jim; University Of California, Berkeley; Pitman@stat.berkeley.edu, Yor, Marc; Université Pierre Et Marie Curie; Pitman@stat.berkeley.edu

Let $M_d$ be the maximum of a standard Bessel bridge of dimension $d$. A series formula for $P(M_d le a)$ due to Gikhman and Kiefer for $d = 1,2, ldots$ is shown to be valid for all real $d >0$....

Laplace transforms related to excursions of a one-dimensional diffusion (1999)

Continuous Martingales and Brownian Motion (1999)

Various known expressions in terms of hyperbolic functions for the Laplace transforms of random times related to one-dimensional Brownian motion are derived in a unified way by excursion theory and...

Revuz, Daniel, Yor, Marc

Libro de probabilidad. Contenido: Introducción; Martingalas; Procesos de Markov; Integración estocástica; Representación de martingalas; Hora media local; Generadores y tiempo de inversión;...

Abel transform and integrals of Bessel local times (1999)

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

Continuous Martingales and Brownian Motion / D. Revuz, M. Yor. (1999)

Revuz, Daniel, Yor, Marc

Libro de probabilidad. Contenido: Introducción; Martingalas; Procesos de Markov; Integración estocástica; Representación de martingalas; Hora media local; Generadores y tiempo de inversión;...

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We obtain some identities in law and some limit theorems for integrals of the type $\int_{0}^{t}\varphi(s)d{\rm L}_{s}$. Here $\varphi$ is a positive locally bounded Borel function and ${\rm L}_{t}$...

Abel transform and integrals of Bessel local times (1999)

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We study integrals of the type $\int_{0}^{t}\varphi(s)dL_{s}$, where $\varphi$ is a positive locally bounded Borel function and $L_{t}$ denotes the local time at level 0 of a Bessel process of...

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We obtain some identities in law and some limit theorems for integrals of the type $\int_{0}^{t}\varphi(s)d{\rm L}_{s}$. Here $\varphi$ is a positive locally bounded Borel function and ${\rm L}_{t}$...

Abel transform and integrals of Bessel local times (1999)

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We study integrals of the type $\int_{0}^{t}\varphi(s)dL_{s}$, where $\varphi$ is a positive locally bounded Borel function and $L_{t}$ denotes the local time at level 0 of a Bessel process of...

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We obtain some identities in law and some limit theorems for integrals of the type $\int_{0}^{t}\varphi(s)d{\rm L}_{s}$. Here $\varphi$ is a positive locally bounded Borel function and ${\rm L}_{t}$...

Abel transform and integrals of Bessel local times (1999)

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We study integrals of the type $\int_{0}^{t}\varphi(s)dL_{s}$, where $\varphi$ is a positive locally bounded Borel function and $L_{t}$ denotes the local time at level 0 of a Bessel process of...

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We obtain some identities in law and some limit theorems for integrals of the type $\int_{0}^{t}\varphi(s)d{\rm L}_{s}$. Here $\varphi$ is a positive locally bounded Borel function and ${\rm L}_{t}$...

Abel transform and integrals of Bessel local times (1999)

Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc

We study integrals of the type $\int_{0}^{t}\varphi(s)dL_{s}$, where $\varphi$ is a positive locally bounded Borel function and $L_{t}$ denotes the local time at level 0 of a Bessel process of...

Laplace transforms related to excursions of a one-dimensional diffusion (1999)

Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions (1999)

Various known expressions in terms of hyperbolic functions for the Laplace transforms of random times related to one-dimensional Brownian motion are derived in a unified way by excursion theory and...

Philippe Biane, Jim Pitman, Marc Yor

This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability...

A Survey and Some Generalizations of Bessel Processes (1999)

Anja Göing-Jaeschke, Marc Yor

Bessel processes play an important role in financial mathematics because of their strong relation to financial processes like geometric Brownian motion or CIR processes. We are interested in the...

Where Did The Brownian Particle Go? (1999)

Robin Pemantle, Yuval Peres, Jim Pitman, Marc Yor

Consider the radial projection onto the unit sphere of the path a d-dimensional Brownian motion W run for unit time. Given the occupation measure ¯ of this projected path, what can be said about the...

On the distribution of ranked heights of excursions of a Brownian bridge (1999)

Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions (1999)

The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge (B br t ; 0 t 1) is described. The height M br+ j of the jth highest...

Philippe Biane, Jim Pitman, Marc Yor

Abstract. This paper reviews known results which connect Riemann’s integral representations of his zeta function, involving Jacobi’s theta function and its derivatives, to some particular...

invariance under a family (1999)

Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading (1999)

properties of the arc-sine law related to its

Ching-tang Wu, Marc Yor

Abstract We consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition as semimartingales in their own filtration. In particular we...

Laplace transforms related to excursions of a one-dimensional diffusion (1999)

Intégrales stochastiques de processus anticipants et projections duales prévisibles (1999)

Various known expressions in terms of hyperbolic functions for the Laplace transforms of random times related to one-dimensional Brownian motion are derived in a uni ed way by excursion theory and...

Yor, Marc, Donati-Martin, C.

We define a stochastic anticipating integral $\delta^\mu$ with respect to Brownian motion, associated to a non adapted increasing process $(\mu_t)$, with dual projection $t$. The integral $\delta^\mu...

Random Brownian scaling identities and splicing of Bessel processes (1998)

Exponential functionals of Brownian motion and disordered systems (1998)

An identity in distribution due to Knight for Brownian motion is extended in two different ways: first by replacing the supremum of a reflecting Brownian motion by the range of an unreflected...

Comtet, Alain, Monthus, Cécile, Yor, Marc

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts, such as continuous time finance models and one-dimensional disordered models. We study...

Perturbed Bessel processes (1998)

Doney, R.A., Warren, Jonathan, Yor, Marc

Autour d'un théorème de Tsirelson sur des filtrations browniennes et non browniennes (1998)

Barlow, Martin T., Émery, Michel, Knight, Frank B., Song, Shiqi, Yor, Marc

Sur un théorème de Tsirelson relatif à des mouvements browniens corrélés et à la nullité de certains temps locaux (1998)

Émery, Michel, Yor, Marc

Quelques calculs de compensateurs impliquant l'injectivité de certains processus croissants (1998)

Azéma, Jacques, Jeulin, Thierry, Knight, Frank B., Yor, Marc

The brownian burglar : conditioning brownian motion by its local time process (1998)

Warren, Jonathan, Yor, Marc

Beta-gamma random variables and intertwining relations between certain Markov processes (1998)

Yor, Marc, Petit, Frédérique, Carmona, Philippe

In this paper, we study particular examples of the intertwining relation Qt? = ?Pt between two Markov semi-groups (Pt, t = 0) defined respectively on (E,e) and (F,F), via the Markov kernel ?: (E,e) ?...

Random Brownian scaling identities and splicing of Bessel processes (1998)

Jim Pitman, Jim Pitman, Marc Yor, Marc Yor

An identity in distribution due to F. Knight for Brownian motion is extended in two different ways: firstly by replacing the supremum of a reflecting Brownian motion by the range of an unreflected...

On the laws of homogeneous functionals of the Brownian bridge (1998)

Philippe Carmona, Erique Petit, Jim Pitman, Marc Yor

Abstract. We develop a general and elementary method, which allows in particular to compute the distributions of a large number of interesting homogeneous functionals of the standard Brownian bridge....

The law of the maximum of a Bessel bridge (1998)

Some Asymptotic Properties of the Local Time of the Uniform Empirical Process (1998)

Let M ffi be the maximum of a standard Bessel bridge of dimension ffi . A series formula for P (M ffi a) due to Gikhman and Kiefer for ffi = 1; 2; : : : is shown to be valid for all real ffi ? 0....

Miklós Csörgo, Org O, Zhan Shi, Marc Yor

this paper we are interested in strong limit theorems for the local time of ff n . We first recall two important results. For notational convenience, we write

Random Brownian scaling identities and splicing of Bessel processes (1998)

Jim Pitman, Jim Pitman, Marc Yor, Marc Yor

An identity in distribution due to F. Knight for Brownian motion is extended in two di erent ways: rstly by replacing the supremum of a re ecting Brownian motion by the range of an unre ected...

Path decompositions of a Brownian bridge related to the ratio of its maximum and amplitude (1998)

The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator (1997)

We give two new proofs of Csaki's formula for the law of the ratio 1, Q of the maximum relative to the amplitude (i.e. the maximum minus minimum) for a standard Brownian bridge. The second of...

On the tails of the supremum and the quadratic variation of strictly local martingales (1997)

The two-parameter Poisson-Dirichlet distribution, denoted $\mathsf{PD}(\alpha, \theta)$ is a probability distribution on the set of decreasing positive sequences with sum 1. The usual...

Elworthy, Kenneth David, Li, Xu-Mei, Yor, Marc

On the lengths of excursions of some Markov processes (1997)

Pitman, James W., Yor, Marc

On the relative lengths of excursions derived from a stable subordinator (1997)

Some remarks about the joint law of brownian motion and its supremum (1997)

Séminaire de Probabilités XXXI / J. Azéma, M. Emery, M. Yor (eds.) (1997)

Azéma, Jacques, Emery, Michel, Yor, Marc

Incluye bibliografía

On the lengths of excursions of some Markov processes (1997)

On the distribution and asymptotic results for exponential functionals of Lévy processes (1997)

Results are obtained regarding the distribution of the ranked lengths of component intervals in the complement of the random set of times when a recurrent Markov process returns to its starting...

Philippe Carmona, Erique Petit, Marc Yor

Abstract. The aim of this note is to study the distribution and the asymptotic behavior of the exponential functional A t:= R t

On the distribution of ranked heights of excursions of a Brownian bridge (1997)

On the distribution of ranked heights of excursions of a Brownian bridge (1997)

The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge (B br t; 0 t 1) is described. The height M br+ j sion of the bridge has...

The two parameter Poisson–Dirichlet (1997)

The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge �B br t � 0 ≤ t ≤ 1 � is described. The height M br+ j of the...

Random Discrete Distributions Derived from Self-Similar Random Sets (1996)

distribution derived from a stable subordinator. by

Pitman, Jim; University Of California, Berkeley; Pitman@stat.berkeley.edu, Yor, Marc; Université Pierre Et Marie Curie; Pitman@stat.berkeley.edu

A model is proposed for a decreasing sequence of random variables $(V_1, V_2, cdots)$ with $sum_n V_n = 1$, which generalizes the Poisson-Dirichlet distribution and the distribution of ranked lengths...

Exponential functionals of Brownian motion and disordered systems (1996)

Comtet, Alain, Monthus, Cécile, Yor, Marc

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts such as continuous time finance models and one-dimensional disordered models. We study...

Exponential functionals of Brownian motion and disordered systems (1996)

Comtet, Alain, Monthus, Cecile, Yor, Marc

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts such as continuous time finance models and one-dimensional disordered models. We study...

Une propriété des martingales pures (1996)

Azéma, Jacques, Rainer, Catherine, Yor, Marc

Sur les processus croissants de type injectif (1996)

Azéma, Jacques, Jeulin, Thierry, Knight, Frank B., Mokobodzki, Gabriel, Yor, Marc

Séminaire de Probabilités XXX / J. Azéma, M. Emery, M. Yor (eds.) (1996)

Azéma, Jacques, Emery, Michel, Yor, Marc

Incluye bibliografía

Exponential functionals of Brownian motion and disordered systems (1996)

Comtet, Alain, Monthus, Cecile, Yor, Marc

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts such as continuous time finance models and one-dimensional disordered models. We study...

Random Discrete Distributions Derived From Self-Similar Random Sets (1996)

: A model is proposed for a decreasing sequence of random variables (V 1 ; V 2 ; \Delta \Delta \Delta) with P n V n = 1, which generalizes the Poisson-Dirichlet distribution and the distribution of...

Markov processes (1996)

To appearinSeminaire de Probabilites XXXI (1996)

On the lengths of excursions of some

The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. (1995)

On the relative lengths of excursions derived from a stable subordinator by

On symmetric stable random variables and matrix transposition (1994)

The two-parameter Poisson-Dirichlet distribution, denoted pd(ff; `), is a distribution on the set of decreasing positive sequences with sum 1. The usual Poisson-Dirichlet distribution with a single...

Donati-Martin, Catherine, Song, Shiqi, Yor, Marc

Séminaire de Probabilités XXVIII / J. Azéma, P. A. Meyer, M. Yor (eds.) (1994)

Moyennes mobiles et semimartingales (1993)

Incluye bibliografía

On the Lévy transformation of brownian motions and continuous martingales (1993)

Dubins, Lester E., Émery, Michel, Yor, Marc

Le théorème d'arrêt en une fin d'ensemble prévisible (1993)

Azéma, Jacques, Jeulin, Thierry, Knight, Frank B., Yor, Marc

Conditional expectations for derivatives of certain stochastic flows (1993)

Elworthy, Kenneth David, Yor, Marc

On an identity in law obtained by A. Földes and P. Révész (1993)

Séminaire de Probabilités XXVII / J. Azéma, P. A. Meyer, M. Yor (eds.) (1993)

Sur les zéros des martingales continues (1992)

Incluye bibliografía

Martingales relatives (1992)

Azéma, Jacques, Meyer, Paul-André, Yor, Marc

Une décomposition non-canonique du drap brownien (1992)

Séminaire de probabilités XXVI / J. Azéma, P.A. Meyer, M. Yor (Eds.) (1992)

A continuous martingale in the plane that may spiral away to infinity (1991)

Incluye bibliografía

Dubins, Lester E., Émery, Michel, Yor, Marc

Une explication du théorème de Ciesielski-Taylor (1991)

Séminaire de probabilités XXV / J. Azéma, P. A. Meyer, M. Yor (eds.) (1991)

Dérivation par rapport au processus de Bessel (1990)

Incluye bibliografía

Filtration des ponts browniens et équations différentielles stochastiques linéaires (1990)

Séminaire de Probabilités XXIV, 1988/89 / J. Azéma, P. A. Meyer, M. Yor (eds.) (1990)

Étude d'une martingale remarquable (1989)

Incluye bibliografía

On Walsh's brownian motions (1989)

Barlow, Martin T., Pitman, Jim, Yor, Marc

Une extension multidimensionnelle de la loi de l'arc sinus (1989)

Barlow, Martin T., Pitman, Jim, Yor, Marc

Mouvement brownien et inégalité de Hardy dans $L^2$ (1989)

Donati-Martin, C., Yor, Marc

Séminaire de probabilités XXIII / édité par J. Azéma, P.A. Meyer et M. Yor (1989)

Remarques sur certaines constructions des mouvements browniens fractionnaires (1988)

Incluye bibliografía

Le mouvement brownien de Lévy indexé par $\mathbb{R}^3$ comme limite centrale de temps locaux d'intersection (1988)

Weinryb, Sophie, Yor, Marc

Sur la loi des temps locaux browniens pris en un temps exponentiel (1988)

Biane, Philippe, Yor, Marc

Séminaire de Probabilités XXII / edité par J. Azéma, P. A. Meyer et M. Yor (1988)

Inégalités pour les processus self-similaires arrêtés à un temps quelconque (1987)

Incluye bibliografía

Song, Shiqi, Yor, Marc

Interprétation d'un calcul de H. Tanaka en théorie générale des processus (1987)

Un processus qui ressemble au pont brownien (1987)

Biane, Philippe, Le Gall, Jean-François, Yor, Marc

Renormalisation et convergence en loi pour certaines intégrales multiples associées au mouvement brownien dans $\mathbb{R}^d$ (1987)

Séminaire de Probabilités XXI / J. Azéma, P. A. Meyer, M. Yor (eds.) (1987)

Précisions sur l'existence et la continuité des temps locaux d'intersection du mouvement brownien dans $\mathbb{R}^2$ (1986)

Incluye bibliografía

Sur la représentation comme intégrales stochastiques des temps d'occupation du mouvement brownien dans $\mathbb{R}^d$ (1986)

Séminaire de Probabilités XX, 1984/85 / edité par J. Azéma et M. Yor (1986)

Stationary excursions (1986)

Incluye bibliografía

Compléments aux formules de Tanaka-Rosen (1985)

Hitting, occupation, and inverse local times of one-dimensional di usions: martingale and

Renormalisation et convergence en loi pour les temps locaux d'intersection du mouvement brownien dans $\mathbb{R}^3$ (1985)

Séminaire de Probabilités XIX / edité par J. Azéma, et M. Yor (eds.) (1985)

Grooissements de filtrations : exemples et applications : séminaire de Calcul Stochastique 1982/83, Université París VI / Edité par Th. Jeulin et M. Yor (1985)

Incluye bibliografía

Yor, Marc, Séminarie De Probabilities

Incluye bibliografía

Séminaire de Probabilités XVIII, 1982/83 / edité par J. Azéma et M. Yor (1984)

Sur l'équation stochastique de Tsirelson (1983)

Incluye bibliografía

Le Gall, Jean-François, Yor, Marc

Le drap brownien comme limite en loi des temps locaux linéaires (1983)

Séminaire de Probabilités XVII, 1981/82 / edité par J. Azéma et M. Yor (1983)

Temps d'arrêt riches et applications (1982)

Incluye bibliografía

Falkner, Neil, Stricker, Christophe, Yor, Marc

Application de la relation de domination à certains renforcements des inégalités de martingales (1982)

Sur la transformée de Hilbert des temps locaux browniens et une extension de la formule d'Itô (1982)

Sur un processus associé aux temps locaux browniens (1982)

Sur les distributions de certaines fonctionnelles du mouvement brownien (1981)

Sur certains commutateurs d'une filtration (1981)

Some remarkable martingales (1981)

Stroock, Daniel W., Yor, Marc

Extrémalité et remplissage de tribus pour certaines martingales purement discontinues (1981)

Lépingle, Dominique, Meyer, Paul-André, Yor, Marc

Introduction au calcul stochastique (1981)

Sur l'intégrabilité uniforme des martingales continues (1980)

Azéma, Jacques, Gundy, Richard F., Yor, Marc

Sur la construction d'une martingale continue de valeur absolue donnée (1980)

Barlow, Martin T., Yor, Marc

Application d'un lemme de Jeulin au grossissement de la filtration brownienne (1980)

Construction d'une martingale réelle continue de filtration naturelle donnée (1980)

Auerhan, J., Lépingle, Dominique, Yor, Marc

Remarques sur une formule de Paul Lévy (1980)

Séminaire de Probabilités XIV, 1978/79 / edite par J. Azéma et M. Yor (1980)

Une solution simple au problème de Skorokhod (1979)

Incluye bibliografía

Inégalité de Hardy, semimartingales, et faux-amis (1979)

Sur l'expression de la dualité entre $H^1$ et $BMO$ (1979)

Quelques épilogues (1979)

En cherchant une définition naturelle des intégrales stochastiques optionnelles (1979)

Les filtrations de certaines martingales du mouvement brownien dans ${\bf R}^n$ (1979)

Sur le balayage des semi-martingales continues (1979)

Sur une formule de la théorie du balayage (1979)

Meyer, Paul-André, Stricker, Christophe, Yor, Marc

Un théorème de J. W. Pitman (1979)

Un exemple de J. Pitman (1979)

Le problème de Skorokhod : compléments à l'exposé précédent (1979)

Grossissement d'une filtration et semi-martingales : théorèmes généraux (1978)

Grossissement d'une filtration et semi-martingales : formules explicites (1978)

Sur certaines propriétés des espaces de Banach $H^1$ et $BMO$ (1978)

Dellacherie, Claude, Meyer, Paul-André, Yor, Marc

Sous-espaces denses dans $L^1$ ou $H^1$ et représentation des martingales (1978)

Yor, Marc, Sam Lazaro, José De

Sur l'extension d'un théorème de Doob à un noyau $\sigma$-fini, d'après G. Mokobodzki (1978)

Yor, Marc, Meyer, Paul-André

Formule de Cauchy relative à certains lacets browniens (1977)

Sur les théories du filtrage et de la prédiction (1977)

À propos d'un lemme de Ch. Yoeurp (1977)

Remarques sur la représentation des martingales comme intégrales stochastiques (1977)

Sur quelques approximations d'intégrales stochastiques (1977)

Étude de certains processus (stochastiquement) différentiables ou holomorphes (1977)

Représentation intégrale de certaines mesures quasi-invariantes sur ${\cal C}({\bf R})$ ; mesures extrémales et propriété de Markov (1976)

Royer, Gilles, Yor, Marc

Sur la théorie de la prédiction (1976)

Yor, Marc, Meyer, Paul-André

Sur les intégrales stochastiques optionnelles et une suite remarquable de formules exponentielles (1976)

Étude de mesures de probabilité sur $C(R^*_+ \,; R)$ quasi invariantes sous les translations de ${\cal D}(R^*_+ \,; R)$ (1975)

Distributions de Frobénius (1975)

On weak Brownian motions of arbitrary order

Canonical decomposition of linear transformations of two independent Brownian motions

Canonical decomposition of linear transformations of two independent Brownian motions

Motivated by the Kyle-Back model of “insider trading”, we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition as...

On weak Brownian motions of arbitrary order

Motivated by the Kyle-Back model of “insider trading”, we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition as...

Séminaire de Probabilités XVI, 1981/82 / edité par J. Azéma et M. Yor

Time Changes for Lévy Processes

Some vols. accompanied by supplements

Hélyette Geman, Dilip B. Madan, Marc Yor

Stochastic Volatility for Lévy Processes

Peter Carr, Hélyette Geman, Dilip B. Madan, Marc Yor

SELF-DECOMPOSABILITY AND OPTION PRICING

Peter Carr, Hélyette Geman, Dilip B. Madan, Marc Yor

Correlation and the pricing of risks

Marc Atlan, Hélyette Geman, Dilip Madan, Marc Yor

Kernel pricing, Change of measure, Catastrophic risk pricing, Self sufficient filtrations, G10, G12, G13,

Stochastic time changes in catastrophe option pricing

Geman, Helyette, Yor, Marc

From planar Brownian windings to Asian options

Stochastic Inequalities and Applications. Evariste Gine, Christian Houdre, and David Nualart

Lévy processes in finance: a remedy to the non-stationarity of continuous martingales

Marc Yor, Boris Leblanc

In this note, we prove that under some minor conditions on $\sigma$, if a martingale $X_t = \int_0^t \sigma_u dW_u $ satisfies, for every given pair $u \geq 0, \, \xi \geq 0$,...

Comments on the life and mathematical legacy of Wolfgang Doeblin

Marc Yor, Bernard Bru

This article contains the translation into English of the main results found in the Comptes Rendus Volume of December 2000, dedicated to Wolfgang Doeblin's sealed envelope sent to the Académie des...

Stochastic volatility, jumps and hidden time changes

Marc Yor, Dilip B. Madan, Hélyette Geman

Stochastic volatility and jumps are viewed as arising from Brownian subordination given here by an independent purely discontinuous process and we inquire into the relation between the realized...

Pricing options on realized variance

Peter Carr, Hélyette Geman, Dilip Madan, Marc Yor

Models which hypothesize that returns are pure jump processes with independent increments have been shown to be capable of capturing the observed variation of market prices of vanilla stock options...

Option prices as probabilities

Madan, D., Roynette, B., Yor, Marc

Four distribution functions are associated with call and put prices seen as functions of their strike and maturity. The random variables associated with these distributions are identified when the...

On an extension of Dufresne's relation between exponential Brownian functionals from opposite drifts to two different drifts: a short proof

Hariya, Yuu, Yor, Marc

In this note, we show how to deduce some relationships between exponential functionals of Brownian motions with two different drifts from the case where the drifts are opposite from each other. We...

Interpretation via Brownian motion of some independence properties between GIG and gamma variables