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Probability Theory and Related Fields

, Volume 144, Issue 1–2, pp 137–177 | Cite as

Averaging principle for a class of stochastic reaction–diffusion equations

  • Sandra CerraiEmail author
  • Mark Freidlin
Article

Abstract

We consider the averaging principle for stochastic reaction–diffusion equations. Under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component, we calculate limiting slow motion. The study of solvability of Kolmogorov equations in Hilbert spaces and the analysis of regularity properties of solutions, allow to generalize the classical approach to finite-dimensional problems of this type in the case of SPDE’s.

Keywords

Stochastic reaction–diffusion equations Invariant measures and ergodicity Averaging principle Kolmogorov equations in Hilbert spaces 

Mathematical Subject Classification (2000).

60F99 60H15 70K65 70K70 37A25 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Dipartimento di Matematica per le DecisioniUniversità di FirenzeFirenzeItaly
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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