A central limit theorem for the stochastic heat equation

Jingyu Huang, David Nualart and Lauri Viitasaari

Stochastic Processes and their Applications, 2020, vol. 130, issue 12, 7170-7184

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.

Keywords: Stochastic heat equation; Central limit theorem; Malliavin calculus; Stein’s method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2020.07.010

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