A central limit theorem for the stochastic heat equation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Huang, Jingyu¹  Nualart, David²  Viitasaari, Lauri³ 

[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

关键词: Stochastic heat equation;    Central limit theorem;    Malliavin calculus;    Stein's method;   

DOI  :  10.1016/j.spa.2020.07.010

来源: Elsevier

【 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.

【 授权许可】

Free