A Central Limit Theorem for the stochastic wave equation with fractional noise

Francisco Delgado-Vences, David Nualart, Guangqu Zheng

Published 2018-12-12Version 1

We study the one-dimensional stochastic wave equation driven by a Gaussian multiplicative noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in [1/2,1)$ in the spatial variable. We show that the normalized spacial average of the solution over $[-R,R]$ converges in total variation distance to a normal distribution, as $R$ tends to infinity. We also provide a functional central limit theorem.