Almost sure central limit theorems for parabolic/hyperbolic Anderson models with Gaussian colored noises

Xia, Panqiu and Zheng, Guangqu 2025. Almost sure central limit theorems for parabolic/hyperbolic Anderson models with Gaussian colored noises. Journal of Theoretical Probability 38 , 46. 10.1007/s10959-025-01412-1

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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.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Springer
ISSN:	0894-9840
Date of First Compliant Deposit:	26 March 2025
Date of Acceptance:	8 March 2025
Last Modified:	23 Apr 2025 11:15
URI:	https://orca.cardiff.ac.uk/id/eprint/177189

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