Averaging principle for a class of stochastic reaction-diffusion equations

被引：130
|
作者：
Cerrai, Sandra [1 ]
Freidlin, Mark [2 ]
机构：
[1] Univ Florence, Dipartimento Matemat Decisioni, I-50134 Florence, Italy
[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2009年 / 144卷 / 1-2期
基金：
美国国家科学基金会;
关键词：
Stochastic reaction-diffusion equations; Invariant measures and ergodicity; Averaging principle; Kolmogorov equations in Hilbert spaces; BEHAVIOR; SYSTEMS;
D O I：
10.1007/s00440-008-0144-z
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
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页码：137 / 177
页数：41
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