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

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Quantitative central limit theorems for the parabolic Anderson model driven by colored noises. / Nualart, David; Xia, Panqiu; Zheng, Guangqu.

In: Electronic Journal of Probability, Vol. 27, 120, 2022.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Nualart, D, Xia, P & Zheng, G 2022, 'Quantitative central limit theorems for the parabolic Anderson model driven by colored noises', Electronic Journal of Probability, vol. 27, 120. https://doi.org/10.1214/22-EJP847

APA

Nualart, D., Xia, P., & Zheng, G. (2022). Quantitative central limit theorems for the parabolic Anderson model driven by colored noises. Electronic Journal of Probability, 27, [120]. https://doi.org/10.1214/22-EJP847

Vancouver

Nualart D, Xia P, Zheng G. Quantitative central limit theorems for the parabolic Anderson model driven by colored noises. Electronic Journal of Probability. 2022;27. 120. https://doi.org/10.1214/22-EJP847

Author

Nualart, David ; Xia, Panqiu ; Zheng, Guangqu. / Quantitative central limit theorems for the parabolic Anderson model driven by colored noises. In: Electronic Journal of Probability. 2022 ; Vol. 27.

Bibtex

@article{60b36dd8dd164f9eb3f3c1f190225067,
title = "Quantitative central limit theorems for the parabolic Anderson model driven by colored noises",
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 Poincar{\'e} 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).",
keywords = "Dalang{\textquoteright}s condition, fractional Brownian motion, Mallivain calculus, parabolic Anderson model, quantitative central limit theorem, second-order Poincar{\'e} inequality, Skorohod integral, Stein method",
author = "David Nualart and Panqiu Xia and Guangqu Zheng",
note = "Publisher Copyright: {\textcopyright} 2022, Institute of Mathematical Statistics. All rights reserved.",
year = "2022",
doi = "10.1214/22-EJP847",
language = "English",
volume = "27",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",

}

RIS

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