An integral inequality for the invariant measure of a stochastic reaction--diffusion equation

Abstract

We consider a reaction--diffusion equation perturbed by noise (not necessarily white). We prove an integral inequality for the invariant measure $\nu$ of a stochastic reaction--diffusion equation. Then we discuss some consequences as an integration by parts formula which extends to $\nu$ a basic identity of the Malliavin Calculus. Finally, we prove the existence of a surface measure for a ball and a half-space of $H$.