Higher Order Fluctuation Expansions for Nonlinear Stochastic Heat Equations in Singular Limits
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911933373874176 |
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| author | Gess, Benjamin Wu, Zhengyan Zhang, Rangrang |
| author_facet | Gess, Benjamin Wu, Zhengyan Zhang, Rangrang |
| contents | Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint scaling regimes of small noise intensity and diverging singularity. The results include both the case of the SHE with regular and irregular diffusion coefficients. In particular, this includes the correlated Dawson-Watanabe and Dean-Kawasaki SPDEs, as well as SPDEs corresponding to the Fleming-Viot and symmetric simple exclusion processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Order Fluctuation Expansions for Nonlinear Stochastic Heat Equations in Singular Limits Gess, Benjamin Wu, Zhengyan Zhang, Rangrang Probability Analysis of PDEs Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint scaling regimes of small noise intensity and diverging singularity. The results include both the case of the SHE with regular and irregular diffusion coefficients. In particular, this includes the correlated Dawson-Watanabe and Dean-Kawasaki SPDEs, as well as SPDEs corresponding to the Fleming-Viot and symmetric simple exclusion processes. |
| title | Higher Order Fluctuation Expansions for Nonlinear Stochastic Heat Equations in Singular Limits |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2406.17892 |