Quantitative central limit theorems for the parabolic Anderson model driven by colored noises
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Quantitative central limit theorems for the parabolic Anderson model driven by colored noises. / Nualart, David; Xia, Panqiu; Zheng, Guangqu.
I: Electronic Journal of Probability, Bind 27, 120, 2022.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Quantitative central limit theorems for the parabolic Anderson model driven by colored noises
AU - Nualart, David
AU - Xia, Panqiu
AU - Zheng, Guangqu
N1 - Publisher Copyright: © 2022, Institute of Mathematical Statistics. All rights reserved.
PY - 2022
Y1 - 2022
N2 - 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).
AB - 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).
KW - Dalang’s condition
KW - fractional Brownian motion
KW - Mallivain calculus
KW - parabolic Anderson model
KW - quantitative central limit theorem
KW - second-order Poincaré inequality
KW - Skorohod integral
KW - Stein method
U2 - 10.1214/22-EJP847
DO - 10.1214/22-EJP847
M3 - Journal article
AN - SCOPUS:85138198329
VL - 27
JO - Electronic Journal of Probability
JF - Electronic Journal of Probability
SN - 1083-6489
M1 - 120
ER -
ID: 344325703