Existence of the Fomin derivative of the invariant measure of a stochastic reaction--diffusion equation - Archive ouverte HAL Access content directly
Conference Papers Year : 2014

Existence of the Fomin derivative of the invariant measure of a stochastic reaction--diffusion equation

Abstract

We consider a reaction--diffusion equation perturbed by noise (not necessarily white). We prove existence of the Fomin derivative of the corresponding transition semigroup $P_t$. The main tool is a new estimate for $P_tD\varphi$ in terms of $\|\varphi\|_{L^2(H,\nu)}$, where $\nu$ is the invariant measure of $P_t$.

Dates and versions

hal-01126707 , version 1 (06-03-2015)

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Giuseppe da Prato, Arnaud Debussche. Existence of the Fomin derivative of the invariant measure of a stochastic reaction--diffusion equation. RIMS Workshop on Mathematical analysis of viscous incompressible fluid, Kyoto University, Nov 2014, Kyoto, Japan. ⟨hal-01126707⟩
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