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

TL;DR

This paper establishes that the weak convergence rate of the averaging principle for a stochastic wave equation with fast oscillations is of order 1, using an asymptotic expansion approach.

Contribution

It provides a rigorous proof of the weak convergence rate of order 1 for stochastic wave equations with fast oscillations, extending averaging principles to this setting.

Findings

Weak convergence rate of order 1 established

Asymptotic expansion approach used for proof

Applicable to stochastic wave equations with oscillations

Abstract

This article deals with the weak errors for averaging principle for a stochastic wave equation in a bounded interval $[0,L]$, perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. Under suitable conditions, it is proved that the rate of weak convergence to the averaged effective dynamics is of order $1$ via an asymptotic expansion approach.