A Khasminskii type averaging principle for stochastic reaction-diffusion equations

TL;DR

This paper extends the classical Khasminskii averaging principle to stochastic reaction-diffusion equations with unbounded noise in any dimension, demonstrating its applicability to infinite-dimensional systems.

Contribution

It introduces a novel extension of the Khasminskii averaging principle to infinite-dimensional stochastic PDEs with unbounded noise.

Findings

Averaging principle holds for a broad class of stochastic reaction-diffusion systems.

Extension of Khasminskii approach from finite to infinite dimensions.

Applicable to systems with unbounded multiplicative noise in any space dimension.

Abstract

We prove that an averaging principle holds for a general class of stochastic reaction-diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite dimensional systems.