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

Giuseppe da Prato (1) , Arnaud Debussche (2, 3)

1 SNS - Scuola Normale Superiore di Pisa
2 IPSO - Invariant Preserving SOlvers
3 IRMAR - Institut de Recherche Mathématique de Rennes

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 $H$.

Mots clés: surface integrals in Hilbert spaces; invariant measures; Fomin differentiability; Reaction diffusion equations

Domaines: Probabilités [math.PR]

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⟩