Averaging 2d stochastic wave equation

Abstract

We consider a 2D stochastic wave equation driven by a Gaussian noise, which is temporally white and spatially colored described by the Riesz kernel. Our first main result is the functional central limit theorem for the spatial average of the solution. And we also establish a quantitative central limit theorem for the marginal and the rate of convergence is described by the total-variation distance. A fundamental ingredient in our proofs is the pointwise $L^p$-estimate of Malliavin derivative, which is of independent interest.

Version2:32pages, restructured, removed Lemma 3.4. and modified Lemma 3.3 (now Lemma 4.3), simplified Step-4, added Remark 3 and (4.8); version 1: 34pages

References in corpus (2)

• Gaussian fluctuations for the stochastic heat equation with colored noise
• Averaging Gaussian functionals

Cited by in corpus (5)

• Central limit theorems for stochastic wave equations in dimensions one and two
• Quantitative central limit theorems for the parabolic Anderson model driven by colored noises
• Stochastic wave equation with Lévy white noise
• Almost sure central limit theorem for the hyperbolic Anderson model with Lévy white noise
• Almost sure central limit theorems for parabolic/hyperbolic Anderson models with Gaussian colored noises