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Journal Articles Journal of Evolution Equations Year : 2017

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 $H$.

Dates and versions

hal-01235038 , version 1 (27-11-2015)

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Giuseppe da Prato, Arnaud Debussche. An integral inequality for the invariant measure of a stochastic reaction--diffusion equation. Journal of Evolution Equations, 2017, 17 (1), pp.197-214. ⟨10.1007/s00028-016-0349-z⟩. ⟨hal-01235038⟩
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