Central limit theorems for nonlinear stochastic wave equations in dimension three
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912179343589376 |
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| author | Ebina, Masahisa |
| author_facet | Ebina, Masahisa |
| contents | In this paper, we consider three-dimensional nonlinear stochastic wave equations driven by the Gaussian noise which is white in time and has some spatial correlations. Using the Malliavin-Stein's method, we prove the Gaussian fluctuation for the spatial average of the solution under the Wasserstein distance in the cases where the spatial correlation is given by an integrable function and by the Riesz kernel. In both cases we also establish functional central limit theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12957 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Central limit theorems for nonlinear stochastic wave equations in dimension three Ebina, Masahisa Probability 60F05, 60G15, 60H07, 60H15 In this paper, we consider three-dimensional nonlinear stochastic wave equations driven by the Gaussian noise which is white in time and has some spatial correlations. Using the Malliavin-Stein's method, we prove the Gaussian fluctuation for the spatial average of the solution under the Wasserstein distance in the cases where the spatial correlation is given by an integrable function and by the Riesz kernel. In both cases we also establish functional central limit theorems. |
| title | Central limit theorems for nonlinear stochastic wave equations in dimension three |
| topic | Probability 60F05, 60G15, 60H07, 60H15 |
| url | https://arxiv.org/abs/2206.12957 |