Stochastic partial differential equations associated with Feller processes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911697479925760 |
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| author | Song, Jian Wang, Meng Yuan, Wangjun |
| author_facet | Song, Jian Wang, Meng Yuan, Wangjun |
| contents | For the stochastic partial differential equation $\frac{\partial u}{\partial t}=\mathcal L u +u\dot W$ where $\dot W$ is Gaussian noise colored in time and $\mathcal L$ is the infinitesimal generator of a Feller process $X$, we obtain Feynman-Kac type of representations for the Stratonovich and Skorohod solutions as well as for their moments. The regularity of the law and the Hölder continuity of the solutions are also studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18726 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stochastic partial differential equations associated with Feller processes Song, Jian Wang, Meng Yuan, Wangjun Probability For the stochastic partial differential equation $\frac{\partial u}{\partial t}=\mathcal L u +u\dot W$ where $\dot W$ is Gaussian noise colored in time and $\mathcal L$ is the infinitesimal generator of a Feller process $X$, we obtain Feynman-Kac type of representations for the Stratonovich and Skorohod solutions as well as for their moments. The regularity of the law and the Hölder continuity of the solutions are also studied. |
| title | Stochastic partial differential equations associated with Feller processes |
| topic | Probability |
| url | https://arxiv.org/abs/2310.18726 |