A central limit theorem for the stochastic heat equation

被引：40

作者：

Huang, Jingyu ^{[1
]}

Nualart, David ^{[2
]}

Viitasaari, Lauri ^{[3
]}

机构：

[1] Univ Birmingham, Sch Math, Birmingham, W Midlands, England

[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[3] Univ Helsinki, Dept Math & Stat, Helsinki, Finland

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2020年 / 130卷 / 12期

关键词：

Stochastic heat equation; Central limit theorem; Malliavin calculus; Stein's method; CHAOTIC CHARACTER;

D O I：

10.1016/j.spa.2020.07.010

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the one-dimensional stochastic heat equation driven by a multiplicative space-time white noise. We show that the spatial integral of the solution from -R to R converges in total variance distance to a standard normal distribution as R tends to infinity, after renormalization. We also show a functional version of this central limit theorem. (C) 2020 Elsevier B.V. All rights reserved.

引用

页码：7170 / 7184

页数：15

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