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

Abstract

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.

arXiv commentV3: Typos fixed, a reference for two-parameter Clark-Ocone formula is added

References in corpus (4)

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• Total variation estimates in the Breuer-Major theorem
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• Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial condition
• Hyperbolic Anderson model with Lévy white noise: spatial ergodicity and fluctuation
• Almost sure central limit theorem for the hyperbolic Anderson model with Lévy white noise
• Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise
• Almost sure central limit theorems for parabolic/hyperbolic Anderson models with Gaussian colored noises
• Pathwise large deviations for white noise chaos expansions
• Spatial stationarity, ergodicity and CLT for parabolic Anderson model with delta initial condition in dimension $d\ge 1$
• Asymptotic properties of the stochastic heat equation in large times