A Khasminskii type averaging principle for stochastic reaction–diffusion equations

A Khasminskii type averaging principle for stochastic reaction–diffusion equations

Sandra Cerrai

Source: Ann. Appl. Probab. Volume 19, Number 3 (2009), 899-948.

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.

Primary Subjects: 60H15, 34C29, 37L40

Keywords: Stochastic reaction diffusion equations; invariant measures; ergodic and strongly mixing processes; averaging principle

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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1245071014
Digital Object Identifier: doi:10.1214/08-AAP560
Mathematical Reviews number (MathSciNet): MR2537194

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