Existence et unicité de diffusions à valeurs dans un espace de Hilbert
Exit times of symmetric stable processes from unbounded convex domains.
Explicit parametrix and local limit theorems for some degenerate diffusion processes
For a class of degenerate diffusion processes of rank 2, i.e. when only Poisson brackets of order one are needed to span the whole space, we obtain a parametrix representation of McKean–Singer [J. Differential Geom.1 (1967) 43–69] type for the density. We therefrom derive an explicit gaussian upper bound and a partial lower bound that characterize the additional singularity induced by the degeneracy. This particular representation then allows to give a local limit theorem with the usual convergence...
Exponential functionals of Brownian motion. II: Some related diffusion processes.
Exponential inequalities for Bessel processes
Extending the Wong-Zakai theorem to reversible Markov processes
We show how to construct a canonical choice of stochastic area for paths of reversible Markov processes satisfying a weak Hölder condition, and hence demonstrate that the sample paths of such processes are rough paths in the sense of Lyons. We further prove that certain polygonal approximations to these paths and their areas converge in -variation norm. As a corollary of this result and standard properties of rough paths, we are able to provide a significant generalization of the classical result...