Multiscale analysis of semilinear damped stochastic wave equations

TL;DR

This paper develops a multiscale analysis framework for semilinear damped stochastic wave equations by integrating sigma convergence with stochastic compactness theorems, deriving an equivalent micro-model.

Contribution

It introduces a novel combination of sigma convergence and stochastic compactness methods for analyzing damped stochastic wave equations.

Findings

Derived an equivalent micro-model for stochastic wave equations.

Established compactness results using Prokhorov and Skorokhod theorems.

Extended multiscale analysis techniques to stochastic PDEs.

Abstract

In this paper we proceed with the multiscale analysis of semilinear damped stochastic wave motions. The analysis is made by combining the well-known sigma convergence method with its stochastic counterpart, associated to some compactness results such as the Prokhorov and Skorokhod theorems. We derive the equivalent model, which is of the same type as the micro-model.