A central limit theorem for the stochastic heat equation

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Huang , J , Nualart , D & Viitasaari , L 2020 , ' A central limit theorem for the stochastic heat equation ' , Stochastic Processes and Their Applications , vol. 130 , no. 12 , pp. 7170-7184 . https://doi.org/10.1016/j.spa.2020.07.010

Title: A central limit theorem for the stochastic heat equation
Author: Huang, Jingyu; Nualart, David; Viitasaari, Lauri
Other contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2020-12
Language: eng
Number of pages: 15
Belongs to series: Stochastic Processes and Their Applications
ISSN: 0304-4149
DOI: https://doi.org/10.1016/j.spa.2020.07.010
URI: http://hdl.handle.net/10138/335658
Abstract: 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.
Subject: Stochastic heat equation
Central limit theorem
Malliavin calculus
Stein's method
CHAOTIC CHARACTER
111 Mathematics
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