EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires
Eigenvalue distribution of random operators and matrices
Elliptic equations of higher stochastic order
This paper discusses analytical and numerical issues related to elliptic equations with random coefficients which are generally nonlinear functions of white noise. Singularity issues are avoided by using the Itô-Skorohod calculus to interpret the interactions between the coefficients and the solution. The solution is constructed by means of the Wiener Chaos (Cameron-Martin) expansions. The existence and uniqueness of the solutions are established under rather weak assumptions, the main of which...
Equality cases in the symmetrization inequalities for Brownian transition functions and Dirichlet heat kernels.
Équation de Burgers avec conditions initiales à accroissements indépendants et homogènes
Équations aux dérivées partielles stochastiques nonlinéaires et solutions de viscosité
Ergodic behaviour of stochastic parabolic equations
The ergodic behaviour of homogeneous strong Feller irreducible Markov processes in Banach spaces is studied; in particular, existence and uniqueness of finite and -finite invariant measures are considered. The results obtained are applied to solutions of stochastic parabolic equations.
Ergodicity for the stochastic complex Ginzburg–Landau equations
Essential m-dissipativity of Kolmogorov operators corresponding to periodic -Navier Stokes equations
We prove the essential m-dissipativity of the Kolmogorov operator associated with the stochastic Navier-Stokes flow with periodic boundary conditions in a space where is an invariant measure
Euler schemes and half-space approximation for the simulation of diffusion in a domain
This paper is concerned with the problem of simulation of , the solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain : namely, we consider the case where the boundary is killing, or where it is instantaneously reflecting in an oblique direction. Given discretization times equally spaced on the interval , we propose new discretization schemes: they are fully implementable and provide a weak error of order under some conditions. The construction...
Euler schemes and half-space approximation for the simulation of diffusion in a domain
This paper is concerned with the problem of simulation of (Xt)0≤t≤T, the solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain D: namely, we consider the case where the boundary ∂D is killing, or where it is instantaneously reflecting in an oblique direction. Given N discretization times equally spaced on the interval [0,T], we propose new discretization schemes: they are fully implementable and provide a weak error of order N-1 under some conditions....
Existence and uniqueness of solutions to a class of stochastic functional partial differential equations via integral contractors.
Existence of quadratic-mean almost periodic solutions to some stochastic hyperbolic differential equations.
Existence of -almost periodic solutions to a class of nonautonomous stochastic evolution equations.
Existence, uniqueness and regularity of parabolic SPDEs driven by Poisson random measure.
Existence, uniqueness and statistical theory of turbulent solutions of the stochastic Navier-Stokes equation, in three dimensions -- an overview.
Explosion en temps fini pour l’équation de Schrödinger non linéaire stochastique surcritique
Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian Systems
We consider a class of 1d Lagrangian systems with random forcing in the spaceperiodic setting: These systems have been studied since the 1990s by Khanin, Sinai and their collaborators [7, 9, 11, 12, 15]. Here we give an overview of their results and then we expose our recent proof of the exponential convergence to the stationary measure [6]. This is the first such result in a classical setting, i.e. in the dual-Lipschitz metric with respect to the Lebesgue space for finite , partially answering...
Extending martingale measure stochastic integral with applications to spatially homogeneous S. P. D. E's.