A Central Limit Theorem for the stochastic heat equation

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.

Cited by in corpus (5)

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• Central limit theorems for stochastic wave equations in dimensions one and two
• High-frequency analysis of parabolic stochastic PDEs with multiplicative noise
• Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise
• Asymptotic properties of the stochastic heat equation in large times