Spatial ergodicity of stochastic wave equations in dimensions 1,2 and 3

TL;DR

This paper proves that solutions to certain stochastic wave equations in one to three dimensions are spatially ergodic, using Malliavin calculus techniques to establish this property.

Contribution

The paper demonstrates spatial ergodicity for a broad class of stochastic wave equations in low dimensions, applying Malliavin calculus in a novel way.

Findings

Solutions are spatially ergodic in dimensions 1, 2, and 3.

Malliavin calculus effectively establishes ergodicity for stochastic wave equations.

Results extend understanding of spatial properties of stochastic PDEs.

Abstract

In this note, we study a large class of stochastic wave equations with spatial dimension less than or equal to $3$. Via a soft application of Malliavin calculus, we establish that their random field solutions are spatially ergodic.