A SIR epidemic model on a refining spatial grid II-Central limit theorem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912149428764672 |
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| author | Gallouët, Thierry Pardoux, Etienne Yeo, Ténan |
| author_facet | Gallouët, Thierry Pardoux, Etienne Yeo, Ténan |
| contents | A stochastic SIR epidemic model taking into account the heterogeneity of the spatial environment is constructed. The deterministic model is given by a partial differential equation and the stochastic one by a space-time jump Markov process. The consistency of the two models is given by a law of large numbers. In this paper, we study the deviation of the spatial stochastic model from the deterministic model by a functional central limit theorem. The limit is a distribution-valued Ornstein-Uhlenbeck Gaussian process, which is the mild solution of a stochastic partial differential equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06480 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A SIR epidemic model on a refining spatial grid II-Central limit theorem Gallouët, Thierry Pardoux, Etienne Yeo, Ténan Probability 60F05, 60G15, 60G65, 60H15, 92D30 A stochastic SIR epidemic model taking into account the heterogeneity of the spatial environment is constructed. The deterministic model is given by a partial differential equation and the stochastic one by a space-time jump Markov process. The consistency of the two models is given by a law of large numbers. In this paper, we study the deviation of the spatial stochastic model from the deterministic model by a functional central limit theorem. The limit is a distribution-valued Ornstein-Uhlenbeck Gaussian process, which is the mild solution of a stochastic partial differential equation. |
| title | A SIR epidemic model on a refining spatial grid II-Central limit theorem |
| topic | Probability 60F05, 60G15, 60G65, 60H15, 92D30 |
| url | https://arxiv.org/abs/2412.06480 |