Asymptotic regimes for the partition into colonies of a branching process with emigration (2009)
We consider a spatial branching process with emigration in which children either remain at the same site as their parents or migrate to new locations and then found their own colonies. We are...
A limit theorem for trees of alleles in branching processes with rare neutral mutations (2009)
We are interested in the genealogical structure of alleles for a Bienaym\'e-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial...
A limit theorem for trees of alleles in branching processes with rare neutral mutations (2009)
We are interested in the genealogical structure of alleles for a Bienaymé-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial...
A limit theorem for trees of alleles in branching processes with rare neutral mutations (2009)
We are interested in the genealogical structure of alleles for a Bienaymé-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial...
A limit theorem for trees of alleles in branching processes with rare neutral mutations (2009)
We are interested in the genealogical structure of alleles for a Bienaymé-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial...
A limit theorem for trees of alleles in branching processes with rare neutral mutations (2009)
We are interested in the genealogical structure of alleles for a Bienaymé-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial...
Asymptotic regimes for the partition into colonies of a branching process with emigration (2009)
We consider a spatial branching process with emigration in which children either remain at the same site as their parents or migrate to new locations and then found their own colonies. We are...
Asymptotic regimes for the partition into colonies of a branching process with emigration (2009)
We consider a spatial branching process with emigration in which children either remain at the same site as their parents or migrate to new locations and then found their own colonies. We are...
The structure of typical clusters in large sparse random configurations (2008)
Bertoin, Jean, Sidoravicius, Vladas
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The...
Two solvable systems of coagulation equations with limited aggregations (2008)
We consider two simple models for the formation of polymers where at the initial time, each monomer has a certain number of potential links (called arms in the text) that are consumed when...
Two solvable systems of coagulation equations with limited aggregations (2008)
We consider two simple models for the formation of polymers where at the initial time, each monomer has a certain number of potential links (called arms in the text) that are consumed when...
Two solvable systems of coagulation equations with limited aggregations (2008)
We consider two simple models for the formation of polymers where at the initial time, each monomer has a certain number of potential links (called arms in the text) that are consumed when...
A system of grabbing particles related to Galton-Watson trees (2008)
Bertoin, Jean, Sidoravicius, Vladas, Vares, Maria Eulalia
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a...
Passage of Lévy Processes across Power Law Boundaries at Small Times (2008)
Bertoin, Jean, Doney, Ronald, Maller, Ross
We wish to characterise when a L\'{e}vy process $X_t$ crosses boundaries like $t^\kappa$, $\kappa>0$, in a one or two-sided sense, for small times $t$; thus, we enquire when $\limsup_{t\downarrow...
Passage of Lévy Processes across Power Law Boundaries at Small Times (2008)
Bertoin, Jean, Doney, Ronald, Maller, Ross
We wish to characterise when a L\'{e}vy process $X_t$ crosses boundaries like $t^\kappa$, $\kappa>0$, in a one or two-sided sense, for small times $t$; thus, we enquire when $\limsup_{t\downarrow...
A system of grabbing particles related to Galton-Watson trees (2008)
Bertoin, Jean, Sidoravicius, Vladas, Eulalia Vares, Maria
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a...
A system of grabbing particles related to Galton-Watson trees (2008)
Bertoin, Jean, Sidoravicius, Vladas, Eulalia Vares, Maria
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a...
The structure of typical clusters in large sparse random configurations (2008)
Bertoin, Jean, Sidoravicius, Vladas
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The...
The structure of typical clusters in large sparse random configurations (2008)
Bertoin, Jean, Sidoravicius, Vladas
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The...
Two solvable systems of coagulation equations with limited aggregations (2008)
We consider two simple models for the formation of polymers where at the initial time, each monomer has a certain number of potential links (called arms in the text) that are consumed when...
Two solvable systems of coagulation equations with limited aggregations (2008)
We consider two simple models for the formation of polymers where at the initial time, each monomer has a certain number of potential links (called arms in the text) that are consumed when...
A system of grabbing particles related to Galton-Watson trees (2008)
Bertoin, Jean, Sidoravicius, Vladas, Eulalia Vares, Maria
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a...
A system of grabbing particles related to Galton-Watson trees (2008)
Bertoin, Jean, Sidoravicius, Vladas, Eulalia Vares, Maria
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a...
We consider a (sub) critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We...
We consider a (sub) critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We...
Jean Bertoin, Jim Pitman, Juan Ruiz, De Chavez
AMS subject classification: 60J65 Conditioned Brownian motion, path transformations We construct a Brownian path conditioned on its minimum value over a fixed time interval by simple transformations...
COMMUNICATIONS in PROBABILITY CONSTRUCTIONS OF A BROWNIAN PATH WITH A GIVEN MINIMUM (2007)
Jean Bertoin, Jim Pitman, Juan Ruiz, De Chavez
AMS subject classification: 60J65 Conditioned Brownian motion, path transformations We construct a Brownian path conditioned on its minimum value over a fixed time interval by simple transformations...
Regenerative embedding of Markov sets (2007)
Jean Bertoin Laboratoire, Jean Bertoin, Only If
this paper. This question also naturally arises in the following more general setting: Suppose Y 1 is a strong Markov process, so the closure M 1 of the set of times when Y 1 visits a xed point, say...
Solutions multifractales de l'équation de Burgers (2007)
Jean Bertoin, Stéphane Jaffard, Et St'ephane Jaffard
Introduction 1.1 Turbulence et Spectre de Singularit'es Nous allons 'etudier certaines solutions de l"equation de Burgers et montrer qu'elles deviennent multifractales. Mais...
Paris Cnrs (umr, J. Bertoin, A. V. Gnedin, Jean Bertoin, Er V. Gnedin
Asymptotic laws for nonconservative self-similar fragmentations
Cedex 05. Asymptotics in Knuth’s parking problem for caravans (2007)
Paris Cnrs (umr, J. Bertoin, G. Miermont, Jean Bertoin, Grégory Miermont
for caravans
Asymptotic regimes for the occupancy scheme of multiplicative cascades (2007)
In the classical occupancy scheme, one considers a fixed discrete probability measure ${\bf p}=(p_i: {i\in{\cal I}})$ and throws balls independently at random in boxes labeled by ${\cal I}$, such...
Asymptotic regimes for the occupancy scheme of multiplicative cascades (2007)
In the classical occupancy scheme, one considers a fixed discrete probability measure ${\bf p}=(p_i: {i\in{\cal I}})$ and throws balls independently at random in boxes labeled by ${\cal I}$, such...
We show that for $0
Reflecting a Langevin Process at an Absorbing Boundary (2007)
We consider a Langevin process with white noise random forcing. We suppose that the energy of the particle is instantaneously absorbed when it hits some fixed obstacle. We show that nonetheless, the...
On prolific individuals in a supercritical continuous state branching process (2007)
Bertoin, Jean, Fontbona, Joaquin, Martinez, Servet
The purpose of this note is to point at an analog for continuous state branching process of the description of prolific individuals in a super-critical Galton-Watson process.
We show that for $0
Asymptotic regimes for the occupancy scheme of multiplicative cascades (2007)
In the classical occupancy scheme, one considers a fixed discrete probability measure ${\bf p}=(p_i: {i\in{\cal I}})$ and throws balls independently at random in boxes labeled by ${\cal I}$, such...
We consider a (sub) critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We...
Reflecting a Langevin Process at an Absorbing Boundary (2007)
We consider a Langevin process with white noise random forcing. We suppose that the energy of the particle is instantaneously absorbed when it hits some fixed obstacle. We show that nonetheless, the...
We consider a (sub) critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We...
Asymptotic regimes for the occupancy scheme of multiplicative cascades (2007)
In the classical occupancy scheme, one considers a fixed discrete probability measure ${\bf p}=(p_i: {i\in{\cal I}})$ and throws balls independently at random in boxes labeled by ${\cal I}$, such...
We show that for $0
On prolific individuals in a supercritical continuous state branching process (2007)
Bertoin, Jean, Fontbona, Joaquin, Martinez, Servet
The purpose of this note is to point at an analog for continuous state branching process of the description of prolific individuals in a super-critical Galton-Watson process.
We consider a (sub) critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We...
We consider a (sub) critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We...
Homogenenous Multitype Fragmentations (2006)
A homogeneous mass-fragmentation, as it has been defined in \cite{RFC}, describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes....
A second order SDE for the Langevin process reflected at a completely inelastic boundary (2006)
It was shown recently that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak...
A second order SDE for the Langevin process reflected at a completely inelastic boundary (2006)
It was shown recently that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak...
A second order SDE for the Langevin process reflected at a completely inelastic boundary (2006)
It was shown recently that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak...
On Continuity Properties of the Law of Integrals of Lévy Processes (2006)
Bertoin, Jean, Lindner, Alexander, Maller, Ross
Let $(\xi,\eta)$ be a bivariate L\'evy process such that the integral $\int_0^\infty e^{-\xi_{t-}} \, d\eta_t$ converges almost surely. We characterise, in terms of their \LL measures, those L\'evy...
On Continuity Properties of the Law of Integrals of Lévy Processes (2006)
Bertoin, Jean, Lindner, Alexander, Maller, Ross
Let $(\xi,\eta)$ be a bivariate L\'evy process such that the integral $\int_0^\infty e^{-\xi_{t-}} \, d\eta_t$ converges almost surely. We characterise, in terms of their \LL measures, those L\'evy...
On Continuity Properties of the Law of Integrals of L\'{e}vy Processes (2006)
Bertoin, Jean, Lindner, Alexander, Maller, Ross A.
Let $(\xi,\eta)$ be a bivariate L\'evy process such that the integral $\int\_0^\infty e^{-\xi\_{t-}} d\eta\_t$ converges almost surely. We characterise, in terms of their \LL measures, those L\'evy...
Passage of Lévy Processes across Power Law Boundaries at Small Times (2006)
Bertoin, Jean, Doney, Ronald, Maller, Ross
We wish to characterise when a L\'{e}vy process $X_t$ crosses boundaries like $t^\kappa$, $\kappa>0$, in a one or two-sided sense, for small times $t$; thus, we enquire when $\limsup_{t\downarrow...
Passage of Lévy Processes across Power Law Boundaries at Small Times (2006)
Bertoin, Jean, Doney, Ronald, Maller, Ross
We wish to characterise when a L\'{e}vy process $X_t$ crosses boundaries like $t^\kappa$, $\kappa>0$, in a one or two-sided sense, for small times $t$; thus, we enquire when $\limsup_{t\downarrow...
Passage of Lévy Processes across Power Law Boundaries at Small Times (2006)
Bertoin, Jean, Doney, Ronald, Maller, Ross
We wish to characterise when a L\'{e}vy process $X_t$ crosses boundaries like $t^\kappa$, $\kappa>0$, in a one or two-sided sense, for small times $t$; thus, we enquire when $\limsup_{t\downarrow...
Passage of L\'evy Processes across Power Law Boundaries at Small Times (2006)
Bertoin, Jean, Doney, Ronald A., Maller, Ross A.
We wish to characterise when a L\'{e}vy process $X_t$ crosses boundaries like $t^\kappa$, $\kappa>0$, in a one or two-sided sense, for small times $t$; thus, we enquire when $\limsup_{t\downarrow...
Reflecting a Langevin Process at an Absorbing Boundary (2006)
We consider a Langevin process with white noise random forcing. We suppose that the energy of the particle is instantaneously absorbed when it hits some fixed obstacle. We show that nonetheless, the...
Reflecting a Langevin Process at an Absorbing Boundary (2006)
We consider a Langevin process with white noise random forcing. We suppose that the energy of the particle is instantaneously absorbed when it hits some fixed obstacle. We show that nonetheless, the...
Reflecting a Langevin Process at an Absorbing Boundary (2006)
We consider a Langevin process with white noise random forcing. We suppose that the energy of the particle is instantaneously absorbed when it hits some fixed obstacle. We show that nonetheless, the...
A second order SDE for the Langevin process reflected at a completely inelastic boundary (2006)
It was shown recently that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak...
On Continuity Properties of the Law of Integrals of Lévy Processes (2006)
Bertoin, Jean, Lindner, Alexander, Maller, Ross
Let $(\xi,\eta)$ be a bivariate L\'evy process such that the integral $\int_0^\infty e^{-\xi_{t-}} \, d\eta_t$ converges almost surely. We characterise, in terms of their \LL measures, those L\'evy...
Asymptotics in Knuth's parking problem for caravans (2006)
Bertoin, Jean, Miermont, Grégory
We consider a generalized version of Knuth's parking problem, in which caravans consisting of a number of cars arrive at random on the unit circle. Then each car turns clockwise until it finds a free...
Homogenenous Multitype Fragmentations (2006)
A homogeneous mass-fragmentation, as it has been defined in \cite{RFC}, describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes....
Asymptotics in Knuth's parking problem for caravans (2006)
Bertoin, Jean, Miermont, Grégory
We consider a generalized version of Knuth's parking problem, in which caravans consisting of a number of cars arrive at random on the unit circle. Then each car turns clockwise until it finds a free...
Homogenenous Multitype Fragmentations (2006)
A homogeneous mass-fragmentation, as it has been defined in \cite{RFC}, describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes....
A second order SDE for the Langevin process reflected at a completely inelastic boundary (2006)
It was shown recently that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak...
On Continuity Properties of the Law of Integrals of Lévy Processes (2006)
Bertoin, Jean, Lindner, Alexander, Maller, Ross
Let $(\xi,\eta)$ be a bivariate L\'evy process such that the integral $\int_0^\infty e^{-\xi_{t-}} \, d\eta_t$ converges almost surely. We characterise, in terms of their \LL measures, those L\'evy...
Exponential functionals of Levy processes (2005)
This text surveys properties and applications of the exponential functional $\int_0^t\exp(-\xi_s)ds$ of real-valued L\'evy processes $\xi=(\xi_t,t\geq0)$.
Stochastic flows associated to coalescent processes III: Limit theorems (2005)
Bertoin, Jean, Le Gall, Jean-François
We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot...
Stochastic flows associated to coalescent processes III: Limit theorems (2005)
Bertoin, Jean, Le Gall, Jean-François
We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot...
Stochastic flows associated to coalescent processes III: Limit theorems (2005)
Bertoin, Jean, Gall, Jean-François Le
We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot...
Bertoin, Jean, Martínez, Servet
Motivated by a problem arising in the mining industry, we estimate the energy 𝓔(η) that is needed to reduce a unit mass to fragments of size at most η in a fragmentation process, when η→0. We...
Asymptotics in Knuth's parking problem for caravans (2005)
Bertoin, Jean, Miermont, Grégory
We consider a generalized version of Knuth's parking problem, in which caravans consisting of a number of cars arrive at random on the unit circle. Then each car turns clockwise until it finds a free...
Asymptotics in Knuth's parking problem for caravans (2005)
Bertoin, Jean, Miermont, Grégory
We consider a generalized version of Knuth's parking problem, in which caravans consisting of a number of cars arrive at random on the unit circle. Then each car turns clockwise until it finds a free...
Asymptotics in Knuth's parking problem for caravans (2005)
Bertoin, Jean, Miermont, Grégory Marc
We consider a generalized version of Knuth's parking problem, in which caravans consisting of a number of cars arrive at random on the unit circle. Then each car turns clockwise until it finds a free...
Different Aspects of a Model for Random Fragmentation Processes (2005)
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques...
Different Aspects of a Model for Random Fragmentation Processes (2005)
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques...
Different Aspects of a Model for Random Fragmentation Processes (2005)
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques...
Exponential functionals of Lévy processes (2005)
This text surveys properties and applications of the exponential functional ∫0texp(−ξs)ds of real-valued Lévy processes ξ=(ξt,t≥0).
Discretization methods for homogeneous fragmentations (2005)
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching...
Discretization methods for homogeneous fragmentations (2005)
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching...
Stochastic flows associated to coalescent processes III: Limit theorems (2005)
Bertoin, Jean, Le Gall, Jean-François
We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot...
Different Aspects of a Model for Random Fragmentation Processes (2005)
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques...
Discretization methods for homogeneous fragmentations (2005)
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching...
Discretization methods for homogeneous fragmentations (2005)
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching...
Stochastic flows associated to coalescent processes III: Limit theorems (2005)
Bertoin, Jean, Le Gall, Jean-François
We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot...
Different Aspects of a Model for Random Fragmentation Processes (2005)
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques...
Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions (2004)
Bertoin, Jean, Roynette, Bernard, Yor, Marc
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)
Bertoin, Jean, Roynette, Bernard, Yor, Marc
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)
Bertoin, Jean, Roynette, Bernard, Yor, Marc
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...
Exponential Functionals of Lévy Processes (2004)
This text surveys properties and applications of the exponential functional $\int_{0}^{t}\exp(-\xi_s)ds$ of real-valued L\'evy processes $\xi=(\xi_t, t\geq0)$.
Exponential Functionals of Lévy Processes (2004)
This text surveys properties and applications of the exponential functional $\int_{0}^{t}\exp(-\xi_s)ds$ of real-valued L\'evy processes $\xi=(\xi_t, t\geq0)$.
Bertoin, Jean, Martinez, Servet
Motivated by a problem arising in mining industry, we estimate the energy ${\cal E}(\eta)$ which is needed to reduce a unit mass to fragments of size at most $\eta$ in a fragmentation process, when...
Bertoin, Jean, Martinez, Servet
Motivated by a problem arising in mining industry, we estimate the energy ${\cal E}(\eta)$ which is needed to reduce a unit mass to fragments of size at most $\eta$ in a fragmentation process, when...
For a subcritical Galton-Watson process $(\zeta_n)$, it is well known that under an $X \log X$ condition, the quotient $P(\zeta_n > 0)/ E\zeta_n$ has a finite positive limit. There is an analogous...
For a subcritical Galton-Watson process $(\zeta_n)$, it is well known that under an $X \log X$ condition, the quotient $P(\zeta_n > 0)/ E\zeta_n$ has a finite positive limit. There is an analogous...
Discretization methods for homogeneous fragmentations (2004)
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching...
For a subcritical Galton-Watson process $(\zeta_n)$, it is well known that under an $X \log X$ condition, the quotient $P(\zeta_n > 0)/ E\zeta_n$ has a finite positive limit. There is an analogous...
Bertoin, Jean, Goldschmidt, Christina
The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains...
Asymptotic Laws for Nonconservative Self-similar Fragmentations (2004)
Bertoin, Jean; Université Paris VI; Jbe@ccr.jussieu.fr, Gnedin, Alexander V.; Rijksuniversiteit Utrecht, The Netherlands; Gnedin@math.uu.nl
We consider a self-similar fragmentation process in which the generic particle of mass $x$ is replaced by the offspring particles at probability rate $x^alpha$, with positive parameter $alpha$. The...
Asymptotic laws for nonconservative self-similar fragmentations (2004)
Bertoin, Jean, Gnedin, Alexander
We consider a self-similar fragmentation process in which the generic particle of size $x$ is replaced at probability rate $x^\alpha$, by its offspring made of smaller particles, where $\alpha$ is...
Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions (2004)
Bertoin, Jean, Roynette, Bernard, Yor, Marc
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...
Exponential Functionals of Lévy Processes (2004)
This text surveys properties and applications of the exponential functional $\int_{0}^{t}\exp(-\xi_s)ds$ of real-valued L\'evy processes $\xi=(\xi_t, t\geq0)$.
Bertoin, Jean, Martinez, Servet
Motivated by a problem arising in mining industry, we estimate the energy ${\cal E}(\eta)$ which is needed to reduce a unit mass to fragments of size at most $\eta$ in a fragmentation process, when...
For a subcritical Galton-Watson process $(\zeta_n)$, it is well known that under an $X \log X$ condition, the quotient $P(\zeta_n > 0)/ E\zeta_n$ has a finite positive limit. There is an analogous...
Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions (2004)
Bertoin, Jean, Roynette, Bernard, Yor, Marc
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...
Exponential Functionals of Lévy Processes (2004)
This text surveys properties and applications of the exponential functional $\int_{0}^{t}\exp(-\xi_s)ds$ of real-valued L\'evy processes $\xi=(\xi_t, t\geq0)$.
Bertoin, Jean, Martinez, Servet
Motivated by a problem arising in mining industry, we estimate the energy ${\cal E}(\eta)$ which is needed to reduce a unit mass to fragments of size at most $\eta$ in a fragmentation process, when...
For a subcritical Galton-Watson process $(\zeta_n)$, it is well known that under an $X \log X$ condition, the quotient $P(\zeta_n > 0)/ E\zeta_n$ has a finite positive limit. There is an analogous...
Path transformations of first passage bridges (2003)
Bertoin, Jean; Universite Pierre Et Marie Curie; Jbe@ccr.jussieu.fr, Chaumont, Loic; Universite Pierre Et Marie Curie; Chaumont@ccr.jussieu.fr, Pitman, Jim; University Of California At Berkeley; Pitman@stat.berkeley.edu
We define the first passage bridge from 0 to $lambda$ as the Brownian motion on the time interval [0,1] conditioned to first hit $lambda$ at time 1. We show that this process may be related to the...
Some aspects of additive coalescents (2003)
We present some aspects of the so-called additive coalescence, with a focus on its connections with random trees, Brownian excursion, certain bridges with exchangeable increments, L\'evy processes,...
Path Transformations of First Passage Bridges (2003)
Paris Cnrs (umr, J. Bertoin, L. Chaumont, J. Pitman, Jean Bertoin, ...
this paper, it follows that conditionally on {B 1 = #}, the process (B 1) has the law of the first passage bridge F # . The next lemma is obtained by following the same arguments as in the proofs of...
Path transformations of first passage bridges (2003)
Jean Bertoin, Loïc Chaumont, Jim Pitman
Summary. We define the first passage bridge from 0 to λ as the Brownian motion on the time interval [0,1] conditioned to first hit λ at time 1. We show that this process may be related to the...
The cornerstone of this work, which is partly motivated by the characterization of the so-called eternal additive coalescents by Aldous and Pitman, is an explicit expression for the general eternal...
Entrance from 0+ for increasing semi-stable Markov processes (2002)
Bertoin, Jean, Caballero, Maria-Emilia
We consider increasing semi-stable Markov processes starting at x>0 and specify their asymptotic behaviour in law as x→0+. This can be viewed as an extension of a result of Brennan and Durrett on...
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...
Eternal additive coalescents and certain bridges with exchangeable increments (2001)
Aldous and Pitman have studied the asymptotic behavior of the additive coalescent processes using a nested family random forests derived by logging certain inhomogeneous continuum random trees. Here...
The Convex Minorant of the Cauchy Process (2000)
Bertoin, Jean; Universite Pierre Et Marie Curie; Jbe@ccr.jussieu.fr
We determine the law of the convex minorant $(M_s, sin [0,1])$ of a real-valued Cauchy process on the unit time interval, in terms of the gamma process. In particular, this enables us to deduce that...
Two coalescents derived from the ranges of stable subordinators (2000)
Let M ff be the closure of the range of a stable subordinator of index ff 2]0; 1[. There are two natural constructions of the M ff 's simultaneously for all ff 2]0; 1[, so that M ff ` M fi for...
Two Coalescents Derived from the Ranges of Stable Subordinators (1999)
Bertoin, Jean; Université Paris VI; Jbe@ccr.jussieu.fr, Pitman, Jim; University Of California, Berkeley; Pitman@stat.berkeley.edu
Let $M_alpha$ be the closure of the range of a stable subordinator of index $alphain ]0,1[$. There are two natural constructions of the $M_{alpha}$'s simultaneously for all $alphain ]0,1[$, so that...
Construction of a Brownian Path With a Given Minimum (1999)
Bertoin, Jean; Universite Pierre Et Marie Curie; Jbe@ccr.jussieu.fr, Pitman, Jim; University Of California, Berkeley; Pitman@stat.Berkeley.EDU, Chavez, Juan Ruiz De; UAM-I; Jrch@xanum.uam.mx
We construct a Brownian path conditioned on its minimum value over a fixed time interval by a simple transformation of a Brownian bridge.
Renewal Theory for Embedded Regenerative Sets (1999)
We consider the age processes $A ^{(1)}\geq\cdots\geq A^{(n)}$ associated to a monotone sequence $\mathscr{R}^{(1)}\subseteq\cdots\subseteq\mathscr{R}^{(n)}$ of regenerative sets. We obtain limit...
On overshoots and hitting times for random walks (1999)
Consider an oscillating integer valued random walk up to the first hitting time of some fixed integer x > 0. Suppose there is a fee to be paid each time the random walk crosses the level x, and that...
Darling-Erdős theorems for normalized sums of i.i.d. variables close to a stable law (1998)
Let $\xi, \xi_1, \dots$ be i.i.d. real-valued random variables and $S_n = \xi_1 + \dots + \xi_n$. In the case when the distribution of $\xi$ is close to a stable $(\alpha)$ law for some $\alpha...
Bertoin, Jean; Université Paris VI; Jbe@ccr.jussieu.fr
Let $X$ be a recurrent Lévy process with no negative jumps and $n$ the measure of its excursions away from $0$. Using Lamperti's connection that links $X$ to a continuous state branching...
Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval (1997)
Consider a completely asymmetric Lévy process which has absolutely continuous transition probabilities. We determine the exponential decay parameter $\rho$ and the quasistationary distribution for...
this paper is devoted to preliminaries on L'evy processes with no negative jumps, continuous state branching processes and the Lamperti connection between the two. The framework is more general...
Bertoin, Jean, Werner, Wendelin
We derive the asymptotic laws of winding numbers for planar isotropic stable Lévy processes and walks of index $\alpha\subset (0,2)$
Jean Bertoin, Jean Bertoin, Jean Bertoin, Wendelin Werner, Wendelin Werner, Wendelin Werner
Stable windings
Iterated Brownian motion and stable() subordinator
We use a connection between the iterated Brownian motion and the stable subordinator of index to derive information on the path behaviour of the former.