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.
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页码：7170 / 7184
页数：15
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