An almost sure central limit theorem for the stochastic heat equation

Jingyu Li and Yong Zhang

Statistics & Probability Letters, 2021, vol. 177, issue C

Abstract: Let u(t,x) be the solution to the stochastic heat equation on R+×Rd driven by a Gaussian noise that is white in time and has a spatially covariance that satisfies Dalang’s condition. In this paper, we prove an almost sure central limit theorem for spatial averages of the form ∫[0,N]dg(u(t,x))dx as N→∞ for fixed t>0, where g is a globally Lipschitz function or belongs to a class of locally Lipschitz functions.

Keywords: Almost sure central limit theorem; Stochastic heat equation; Malliavin calculus; Poincaré-type inequality (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109149

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