Moderate deviations for a stochastic wave equation in dimension three

TL;DR

This paper establishes a central limit theorem and a moderate deviation principle for a three-dimensional stochastic wave equation driven by Gaussian noise, using the weak convergence approach.

Contribution

It introduces the first moderate deviation principle for a stochastic wave equation in three dimensions with Gaussian noise.

Findings

Proved a central limit theorem for the equation.

Established a moderate deviation principle.

Applied the weak convergence approach effectively.

Abstract

In this paper, we proved a central limit theorem and established a moderate deviation principle for a perturbed stochastic wave equation defined on $[0,T]\times \rr^3$. This equation is driven by a Gaussian noise, white in time and correlated in space. The weak convergence approach plays an important role.