Weak order in averaging principle for stochastic wave equation with a fast oscillation

This article deals with the weak error in averaging principle for a stochastic wave equation on a bounded interval [0,L], perturbed by an oscillating term arising as the solution of a stochastic reaction–diffusion equation evolving on the fast time scale. Under suitable conditions, it is proved that...

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Bibliographic Details
Published in:Stochastic processes and their applications 2018-08, Vol.128 (8), p.2557-2580
Main Authors: Fu, Hongbo, Wan, Li, Liu, Jicheng, Liu, Xianming
Format: Article
Language:English
Subjects:
Asymptotic expansion
Averaging principle
Invariant measure
Stochastic wave equation
Weak convergence
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Summary:This article deals with the weak error in averaging principle for a stochastic wave equation on a bounded interval [0,L], perturbed by an oscillating term arising as the solution of a stochastic reaction–diffusion equation evolving on the fast time scale. Under suitable conditions, it is proved that the rate of weak convergence of the original solution to the solution of the corresponding averaged equation is of order 1 via an asymptotic expansion approach.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2017.09.021