Gaussian fluctuations of spatial averages of a system of stochastic heat equations

David Nualart; Bhargobjyoti Saikia

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arXiv · 2211.06551

Gaussian fluctuations of spatial averages of a system of stochastic heat equations

David Nualart·Bhargobjyoti Saikia

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Abstract

We consider a system of $d$ non-linear stochastic heat equations driven by an $m$-dimensional space-time white noise on $\mathbb{R}_+\times \mathbb{R}$. In this paper we study the asymptotic behavior of spatial averages over large intervals $[-R,R]$. We establish a rate of convergence to a multivariate normal distribution in the Wasserstein distance and a functional central limit theorem.

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David Nualart, Bhargobjyoti Saikia. 2022-11-12. Gaussian fluctuations of spatial averages of a system of stochastic heat equations. https://arxiv.org/abs/2211.06551

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