Parabolic SPDEs degenerating on the boundary of nonsmooth domain.
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.
Periodic in distribution solution for a telegraph equation.
Petites perturbations de systèmes dynamiques avec réflexion
Positivity of the density for the stochastic wave equation in two spatial dimensions
We consider the random vector , where are distinct points of and denotes the stochastic process solution to a stochastic wave equation driven by a noise white in time and correlated in space. In a recent paper by Millet and Sanz–Solé [10], sufficient conditions are given ensuring existence and smoothness of density for . We study here the positivity of such density. Using techniques developped in [1] (see also [9]) based on Analysis on an abstract Wiener space, we characterize the set of...
Positivity of the density for the stochastic wave equation in two spatial dimensions
We consider the random vector , where t > 0, x1,...,xd are distinct points of and u denotes the stochastic process solution to a stochastic wave equation driven by a noise white in time and correlated in space. In a recent paper by Millet and Sanz–Solé [10], sufficient conditions are given ensuring existence and smoothness of density for . We study here the positivity of such density. Using techniques developped in [1] (see also [9]) based on Analysis on an abstract Wiener space, we characterize...
Probabilistic analysis of singularities for the 3-D Navier-Stokes equations
Probabilistic analysis of singularities for the 3D Navier-Stokes equations
The classical result on singularities for the 3D Navier-Stokes equations says that the -dimensional Hausdorff measure of the set of singular points is zero. For a stochastic version of the equation, new results are proved. For statistically stationary solutions, at any given time , with probability one the set of singular points is empty. The same result is true for a.e. initial condition with respect to a measure related to the stationary solution, and if the noise is sufficiently non degenerate...
Probabilistic interpretation of a system of semi-linear parabolic partial differential equations
Probability density for a hyperbolic SPDE with time dependent coefficients
We prove the existence and smoothness of density for the solution of a hyperbolic SPDE with free term coefficients depending on time, under hypoelliptic non degeneracy conditions. The result extends those proved in Cattiaux and Mesnager, PTRF123 (2002) 453-483 to an infinite dimensional setting.
Probability structure preserving and absolute continuity
Problèmes de temps d'arrêt optimal pour les systèmes distribués stochastiques
Processus associés à l'équation des milieux poreux
Propagation of chaos for Burgers' equation
Propagation of elastic waves in DNA.
Prospective Kolmogorov equation of non-Markovian stochastic processes