Fabrice Baudoin

On gradient bounds for the heat kernel on the Heisenberg group

It is known that the couple formed by the two dimensional Brownian motion and its Levy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The associated diffusion operator is hypoelliptic but not elliptic, which makes difficult the derivation of functional inequalities for the heat kernel. However, Driver and Melcher and more recently H.-Q. Li have obtained useful gradient bounds for the heat kernel on the Heisenberg group. We provide in this paper simple proofs of these bounds, and explore their consequences in terms of functional inequalities, including Cheeger and Bobkov type isoperimetric inequalities for the heat kernel.

Equivalence of Volterra processes

In this paper we study necessary and sufficient conditions for the equivalence of Volterra Gaussian processes. Though this topic has already been studied in the literature, we provide new proofs, precisions and new theorems. We also give some examples of equivalent Volterra processes all related to the extensively studied fractional Brownian motion. Finally, we give an extension to general Gaussian processes of a recent regularization theorem by P. Cheridito.

The subelliptic heat kernel on the CR sphere

We study the heat kernel of the sub-Laplacian

Hypoellipticity in infinite dimensions and an application in interest rate theory

L

Modeling Anticipations on Financial Markets

on the CR sphere

Stochastic analysis on sub-Riemannian manifolds with transverse symmetries

\mathbb{S }^{2n+1}