Flows for the stochastic Navier-Stokes equation.
Formule de Ito pour des processus non continus à valeurs dans des espaces de Banach
Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise
We consider an initial and Dirichlet boundary value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. Discretizing the space-time white noise a modelling error is introduced and a regularized fourth-order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a Galerkin finite element method...
Functional integro-differential stochastic evolution equations in Hilbert space.
Galerkin approximation and the strong solution of the Navier-Stokes equation.
Generalized functionals of Brownian motion.
Generalized random processes and Cauchy's problem for some partial differential systems.
Generic solvability for the 3-D Navier-Stokes equations with nonregular force.
Géométrie différentielle stochastique, II
Hitting properties of a random string.
Homogenization and ergodic theory
Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [Probab. Theory Related Fields (2009)] and improves this latter work by...
Homotopy and Homology Vanishing Theorems and the Stability of Stochastic Flows.
Hypercontractivity of solutions to Hamilton-Jacobi equations
We show that solutions to some Hamilton-Jacobi Equations associated to the problem of optimal control of stochastic semilinear equations enjoy the hypercontractivity property.
Infinite system of Brownian balls with interaction: the non-reversible case
We consider an infinite system of hard balls in undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.
Initial measures for the stochastic heat equation
We consider a family of nonlinear stochastic heat equations of the form , where denotes space–time white noise, the generator of a symmetric Lévy process on , and is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure . Tight a priori bounds on the moments of the solution are also obtained. In the particular case that for some , we prove that if is a finite measure of compact support, then the solution is...
Integral inequality and exponential stability for neutral stochastic partial differential equations with delays.
Intermittence and nonlinear parabolic stochastic partial differential equations.
Intermittency properties in a hyperbolic Anderson problem
We study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension 3 with linear multiplicative spatially homogeneous gaussian noise that is white in time. Our main theorem states that these moments grow more quickly than one might expect. This phenomenon is well known for parabolic stochastic partial differential equations, under the name of intermittency. Our results seem to be the first example of this phenomenon for hyperbolic equations. For comparison,...
Introduction au calcul stochastique