Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912421311938560 |
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| author | Baudoin, Fabrice Chen, Hongyi Ouyang, Cheng |
| author_facet | Baudoin, Fabrice Chen, Hongyi Ouyang, Cheng |
| contents | We study the effect of curvature on the Parabolic Anderson model by posing it over a Cartan-Hadamard manifold. We first construct a family of noises white in time and colored in space parameterized by a regularity parameter $α$, which we use to explore regularity requirements for well-posedness. Then, we show that conditions on the heat kernel imply an exponential in time upper bound for the moments of the solution, and a lower bound for sectional curvature imply a corresponding lower bound. These results hold if the noise is strong enough, where the needed strength of the noise is affected by sectional curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds Baudoin, Fabrice Chen, Hongyi Ouyang, Cheng Probability We study the effect of curvature on the Parabolic Anderson model by posing it over a Cartan-Hadamard manifold. We first construct a family of noises white in time and colored in space parameterized by a regularity parameter $α$, which we use to explore regularity requirements for well-posedness. Then, we show that conditions on the heat kernel imply an exponential in time upper bound for the moments of the solution, and a lower bound for sectional curvature imply a corresponding lower bound. These results hold if the noise is strong enough, where the needed strength of the noise is affected by sectional curvature. |
| title | Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds |
| topic | Probability |
| url | https://arxiv.org/abs/2411.09614 |