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

Files
2409.07358v2.pdf(279.77 KB)
Accepted manuscript
Date
2025-06
DOI
10.48550/arXiv.2409.07358
Authors
Version
Accepted manuscript
URI
https://hdl.handle.net/2144/50190
OA Version
Citation
G. Zheng, P. XIA. 2025. "Almost sure central limit theorems for parabolic/hyperbolic Anderson models with Gaussian colored noises" Journal of Theoretical Probability, Volume 38, Issue 2. https://doi.org/10.1007/s10959-025-01412-1
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.
Description
License
This article is distributed under the terms of the Creative Commons Attribution 4.0 International.
cb
Collections
BU Open Access Articles