The Annals of Applied Probability

A Khasminskii type averaging principle for stochastic reaction–diffusion equations

Sandra Cerrai

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 15 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1245071014

Digital Object Identifier
doi:10.1214/08-AAP560

Mathematical Reviews number (MathSciNet)
MR2537194

Zentralblatt MATH identifier
1191.60076

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 34C29: Averaging method 37L40: Invariant measures

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

Citation

Cerrai, Sandra. A Khasminskii type averaging principle for stochastic reaction–diffusion equations. Ann. Appl. Probab. 19 (2009), no. 3, 899--948. doi:10.1214/08-AAP560. https://projecteuclid.org/euclid.aoap/1245071014


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