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.