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

We consider a reaction–diffusion equation perturbed by noise (not necessarily white). We prove an integral inequality for the invariant measure ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\nu}$$\end{document} of a stochastic reaction–diffusion equation. Then, we discuss some consequences as an integration by parts formula which extends to ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\nu}$$\end{document} 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.