Averaging principle and normal deviations for multi-scale stochastic hyperbolic–parabolic equations

被引：0
作者：
Michael Röckner
Longjie Xie
Li Yang
机构：
[1] Universität Bielefeld,Fakultät für Mathematik
[2] Chinese Academy of Sciences (CAS),Academy of Mathematics and Systems Science
[3] Jiangsu Normal University,School of Mathematics and Statistics
[4] Shandong University,School of Mathematics
来源：
Stochastics and Partial Differential Equations: Analysis and Computations | 2023年 / 11卷
关键词：
Stochastic hyperbolic–parabolic equations; Averaging principle; Strong and weak convergence; Homogenization; 60H15; 60F05; 70K70;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the asymptotic behavior of stochastic hyperbolic–parabolic equations with slow–fast time scales. Both the strong and weak convergence in the averaging principle are established. Then we study the stochastic fluctuations of the original system around its averaged equation. We show that the normalized difference converges weakly to the solution of a linear stochastic wave equation. An extra diffusion term appears in the limit which is given explicitly in terms of the solution of a Poisson equation. Furthermore, sharp rates for the above convergence are obtained, which are shown not to depend on the regularity of the coefficients in the equation for the fast variable.
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页码：869 / 907
页数：38
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