Gaussian fluctuations of spatial averages of a system of stochastic heat equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909370965557248 |
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| author | Nualart, David Saikia, Bhargobjyoti |
| author_facet | Nualart, David Saikia, Bhargobjyoti |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06551 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Gaussian fluctuations of spatial averages of a system of stochastic heat equations Nualart, David Saikia, Bhargobjyoti Probability 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. |
| title | Gaussian fluctuations of spatial averages of a system of stochastic heat equations |
| topic | Probability |
| url | https://arxiv.org/abs/2211.06551 |