Baudoin, Fabrice, Bonnefont, Michel, Garofalo, Nicola
We prove that on rank two sub-Riemannian manifolds with non negative Ricci curvature in the sense of Baudoin-Garofalo, the following properties hold: 1) The volume doubling property; 2) The Poincare...
Baudoin, Fabrice, Ouyang, Cheng
In this paper we show that under some assumptions, for a $d$-dimensional fractional Brownian motion with Hurst parameter $H>1/2$, the density of solution of stochastic differential equation driven by...
Perelman's entropy and doubling property on Riemannian manifolds (2009)
Baudoin, Fabrice, Garofalo, Nicola
The purpose of this work is to study some monotone functionals of the heat kernel on a complete Riemannian manifold with nonnegative Ricci curvature. In particular, we show that on these manifolds,...
Stochastic Taylor expansions and heat kernel asymptotics (2009)
These notes focus on the applications of the stochastic Taylor expansion of solutions of stochastic differential equations to the study of heat kernels in small times. As an illustration of these...
Generalized Bochner formulas and Ricci lower bounds for sub-Riemannian manifolds of rank two (2009)
Baudoin, Fabrice, Garofalo, Nicola
We study a new class of rank two sub-Riemannian manifolds encompassing Riemannian manifolds, CR manifolds with vanishing Webster-Tanaka torsion, orthonormal bundles over Riemannian manifolds, and...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its Lévy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its Lévy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
Exponential functionals of Brownian motion and class one Whittaker functions (2008)
Baudoin, Fabrice, O'Connell, Neil
We consider exponential functionals of a multi-dimensional Brownian motion with drift, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their...
Self-similarity and fractional Brownian motion on Lie groups (2008)
Baudoin, Fabrice; Institut De Mathématiques, Toulouse; Fbaudoin@cict.fr, Coutin, Laure; Universite Paris 5; Laure.Coutin@math-info.univ-paris5.fr
The goal of this paper is to define and study a notion of fractional Brownian motion on a Lie group. We define it as at the solution of a stochastic differential equation driven by a linear...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds (2008)
Baudoin, Fabrice, Bonnefont, Michel
The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its Lévy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its Lévy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
Subelliptic Li-Yau estimates on three dimensional model spaces (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Qian, Bin
We describe three elementary models in three dimensional subelliptic geometry which corresponds to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which...
Subelliptic Li-Yau estimates on three dimensional model spaces (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Qian, Bin
We describe three elementary models in three dimensional subelliptic geometry which corresponds to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which...
Subelliptic Li-Yau estimates on three dimensional model spaces (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Qian, Bin
We describe three elementary models in three dimensional subelliptic geometry which corresponds to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its Lévy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
Subelliptic Li-Yau estimates on three dimensional model spaces (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Qian, Bin
We describe three elementary models in three dimensional subelliptic geometry which corresponds to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which...
Subelliptic Li-Yau estimates on three dimensional model spaces (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Qian, Bin
We describe three elementary models in three dimensional subelliptic geometry which corresponds to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which...
On gradient bounds for the heat kernel on the Heisenberg group (2007)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2007)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
Ornstein-Uhlenbeck Processes on Lie Groups (2007)
Baudoin, Fabrice, Hairer, Martin, Teichmann, Josef
We consider Ornstein-Uhlenbeck processes (OU-processes) associated to hypoelliptic diffusion processes on finite-dimensional Lie groups: let $ \mathcal{L} $ be a hypoelliptic, left-invariant ``sum of...
On gradient bounds for the heat kernel on the Heisenberg group (2007)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2007)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
Chen series and Atiyah-Singer index theorem (2006)
The purpose of this work is to give a new and short proof of Atiyah-Singer local index theorem by using heat semigroups approximations based on the truncature of Brownian Chen series.
Notes on the two-dimensional fractional Brownian motion (2006)
Baudoin, Fabrice, Nualart, David
We study the two-dimensional fractional Brownian motion with Hurst parameter $H>{1/2}$. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and...
Notes on the two-dimensional fractional Brownian motion (2006)
Baudoin, Fabrice, Nualart, David
We study the two-dimensional fractional Brownian motion with Hurst parameter H>½. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce...
Baudoin, Fabrice, Coutin, Laure
In this paper, by using a Taylor development type formula, we show how it is possible to associate differential operators with stochastic differential equations driven by a fractional Brownian...
Hypoellipticity in infinite dimensions and an application in interest rate theory (2005)
Baudoin, Fabrice, Teichmann, Josef
We apply methods from Malliavin calculus to prove an infinite-dimensional version of Hormander's theorem for stochastic evolution equations in the spirit of Da Prato-Zabczyk. This result is used to...
Hypoellipticity in infinite dimensions and an application in interest rate theory (2005)
Baudoin, Fabrice, Teichmann, Josef
We apply methods from Malliavin calculus to prove an infinite-dimensional version of Hörmander’s theorem for stochastic evolution equations in the spirit of Da Prato–Zabczyk. This result is used...
Conditioning and initial enlargement of filtration on a Riemannian manifold (2004)
We extend to Riemannian manifolds the theory of conditioned stochastic differential equations. We also provide some enlargement formulas for the Brownian filtration in this nonflat setting.
Conditioning and initial enlargement of filtration on a Riemannian manifold (2004)
We extend to Riemannian manifolds the theory of conditioned stochastic differential equations. We also provide some enlargement formulas for the Brownian filtration in this nonflat setting.
We generalize the notion of brownian bridge. More precisely, we study a standard brownian motion for which a certain functional is conditioned to follow a given law. Such processes appear as weak...
Further Exponential Generalization of Pitman's 2M-X Theorem (2002)
Baudoin, Fabrice; Université Paris 6 Et Paris 7; Baudoin@ensae.fr
We present a class of processes which enjoy an exponential analogue of Pitman's 2M-X theorem, improving hence some works of H. Matsumoto and M. Yor.
Further Exponential Generalization of Pitman's 2M-X Theorem (2002)
Baudoin, Fabrice; Université Paris 6 Et Paris 7; Baudoin@ensae.fr
We present a class of processes which enjoy an exponential analogue of Pitman's 2M-X theorem, improving hence some works of H. Matsumoto and M. Yor.
Portfolio optimization associated with a weak information (2001)
In this paper we consider an investor who trades in a complete financial market so as to maximize his expected utility of wealth at a prespecified time. We assume that he is in the following position...
The financial value of a weak information on a financial market
Fabrice Baudoin, Laurent Nguyen-Ngoc
The results of [4] are extended under weaker assumptions to d-dimensional and possibly discontinuous processes and applied to the modelling of weak anticipations both on complete and incomplete...