Parabolic SPDEs degenerating on the boundary of nonsmooth domain.
Path properties of a class of locally asymptotically self similar processes.
Pathwise uniqueness for stochastic PDEs
We consider a stochastic evolution equation in a separable Hilbert spaces H or in a separable Banach space E with a Hölder continuous perturbation on the drift. We review some recent result about pathwise uniqueness for this equation.
Periodic and invariant measures for stochastic wave equations.
Perturbation theory for random walk in asymmetric random environment.
Probabilistic well-posedness for the cubic wave equation
The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We restrict the study to one of the simplest examples of such equations: the periodic cubic semi-linear wave equation. Our contributions in this work are twofold: first we break the algebraic rigidity involved in our previous works and allow much more general randomizations (general infinite product measures v.s. Gibbs...
Propagation of chaos for the 2D viscous vortex model
We consider a stochastic system of particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly...