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Gaussian fluctuations of spatial averages of a system of stochastic heat equations
David Nualart, Bhargobjyoti Saikia · 2022-11-12 · via math.PR updates on arXiv.org

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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