Fokker-Planck equation for McKean-Vlasov SPDEs driven by time-space Brownian sheet
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914777636274176 |
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| author | Agram, Nacira Oksendal, Bernt Proske, Frank Tymoshenko, Olena |
| author_facet | Agram, Nacira Oksendal, Bernt Proske, Frank Tymoshenko, Olena |
| contents | In this paper, we consider a McKean-Vlasov (mean-field) stochastic partial differential equations (SPDEs) driven by a Brownian sheet. We study the propagation of chaos for a space-time Ornstein-Uhlenbeck SPDE type. Subsequently, we prove the existence and uniqueness of a nonlinear McKean-Vlasov SPDE. Finally, we establish a Fokker-Planck equation for the law of the solution of the McKean-Vlasov type SPDE driven by a time-space Brownian sheet, and we provide some examples to illustrate the results obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19490 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fokker-Planck equation for McKean-Vlasov SPDEs driven by time-space Brownian sheet Agram, Nacira Oksendal, Bernt Proske, Frank Tymoshenko, Olena Probability In this paper, we consider a McKean-Vlasov (mean-field) stochastic partial differential equations (SPDEs) driven by a Brownian sheet. We study the propagation of chaos for a space-time Ornstein-Uhlenbeck SPDE type. Subsequently, we prove the existence and uniqueness of a nonlinear McKean-Vlasov SPDE. Finally, we establish a Fokker-Planck equation for the law of the solution of the McKean-Vlasov type SPDE driven by a time-space Brownian sheet, and we provide some examples to illustrate the results obtained. |
| title | Fokker-Planck equation for McKean-Vlasov SPDEs driven by time-space Brownian sheet |
| topic | Probability |
| url | https://arxiv.org/abs/2404.19490 |