A Central Limit Theorem for the stochastic heat equation

Jingyu Huang; David Nualart; Lauri Viitasaari

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arXiv · 1810.09492

A Central Limit Theorem for the stochastic heat equation

Jingyu Huang·David Nualart·Lauri Viitasaari

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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.

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Jingyu Huang, David Nualart, Lauri Viitasaari. 2018-10-22. A Central Limit Theorem for the stochastic heat equation. https://arxiv.org/abs/1810.09492

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