Invariant measures for monotone SPDE's with multiplicative noise term

TL;DR

This paper investigates invariant measures for certain infinite-dimensional stochastic PDEs with multiplicative noise, establishing existence results and applying them to stochastic reaction diffusion equations.

Contribution

It proves the existence of invariant measures for monotone SPDEs with multiplicative noise, extending previous results to more general diffusion coefficients.

Findings

Existence of invariant measures for the studied SPDEs.

Proved tightness and Feller property of solutions.

Application to stochastic reaction diffusion equations.

Abstract

We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller property of the solution to show existence of an invariant measure. As an application we discuss stochastic reaction diffusion equations.