Quantitative central limit theorems for the parabolic Anderson model driven by colored noises

Nualart, David, Xia, Panqiu and Zheng, Guangqu 2022. Quantitative central limit theorems for the parabolic Anderson model driven by colored noises. Electronic Journal of Probability 27 , pp. 1-43. 10.1214/22-ejp847

Preview

PDF - Published Version Available under License Creative Commons Attribution. Download (668kB) | Preview

Abstract

In this paper, we study the spatial averages of the solution to the parabolic Anderson model driven by a space-time Gaussian homogeneous noise that is colored in both time and space. We establish quantitative central limit theorems (CLT) of this spatial statistics under some mild assumptions, by using the Malliavin-Stein approach. The highlight of this paper is the obtention of rate of convergence in the colored-in-time setting, where one can not use Ito calculus due to the lack of martingale structure. In particular, modulo highly technical computations, we apply a modified version of second-order Gaussian Poincaré inequality to overcome this lack of martingale structure and our work improves the results by Nualart-Zheng (Electron. J. Probab. 2020) and Nualart-Song-Zheng (ALEA, Lat. Am. J. Probab. Math. Stat. 2021).

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Institute of Mathematical Statistics
ISSN:	1083-6489
Date of First Compliant Deposit:	2 September 2024
Date of Acceptance:	31 August 2022
Last Modified:	02 Sep 2024 16:00
URI:	https://orca.cardiff.ac.uk/id/eprint/171080

Actions (repository staff only)

Edit Item