Almost Sure Central Limit Theorems for Parabolic/Hyperbolic Anderson Models with Gaussian Colored Noises

Panqiu Xia () and Guangqu Zheng ()
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Panqiu Xia: Cardiff University
Guangqu Zheng: Boston University

Journal of Theoretical Probability, 2025, vol. 38, issue 2, 1-22

Abstract: Abstract This short note is devoted to establishing the almost sure central limit theorem for the parabolic/hyperbolic Anderson models driven by colored-in-time Gaussian noises, completing recent results on quantitative central limit theorems for stochastic partial differential equations. We combine the second-order Gaussian Poincaré inequality with the method of characteristic functions of Ibragimov and Lifshits, effectively overcoming the challenge from the lack of Itô tools in this colored-in-time setting, and achieving results that are inaccessible with previous methods.

Keywords: Almost sure central limit theorem; Hyperbolic Anderson model; Parabolic Anderson model; criterion of Ibragimov and Lifshits; Second-order Gaussian Poincaré inequality; Malliavin calculus; Space-time colored noises; 60F15; 60H30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01412-1

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