Almost sure central limit theorems for stochastic wave equations

Abstract

In this paper, we study almost sure central limit theorems for the spatial average of the solution to the stochastic wave equation in dimension $d\le 2$ over a Euclidean ball, as the radius of the ball diverges to infinity. This equation is driven by a general Gaussian multiplicative noise, which is temporally white and colored in space including the cases of the spatial covariance given by a fractional noise, a Riesz kernel, and an integrable function that satisfies Dalang’s condition.