We prove existence and (in some special case) uniqueness of an invariant measure for the transition semigroup associated with the stochastic wave equations with nonlinear dissipative damping.

We prove, using coupling arguments, exponential convergence to equilibrium for reaction-diffusion and Burgers equations driven by space-time white noise. We use a coupling by reflection.

We prove the existence of an invariant measure [mu] for the transition semigroup Pt associated with the fast diffusion porous media equation in a bounded domain , perturbed by a Gaussian noise. The Kolmogorov infinitesimal generator N of Pt in is characterized as the closure of a second-order...

The aim of this article is to study the asymptotic behavior for large times of solutions of linear stochastic partial differential equations of parabolic type. In particular, we will prove the backward uniqueness result and the existence of the spectral limit for abstract SPDEs and then show how...