McKean–Vlasov type stochastic differential equations arising from the random vortex method
We study a class of McKean–Vlasov type stochastic differential equations (SDEs) which arise from the random vortex dynamics and other physics models. By introducing a new approach we resolve the existence and uniqueness of both the weak and strong solutions for the McKean–Vlasov stochastic different...
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| Format: | Journal article |
| Language: | English |
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Springer
2021
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| _version_ | 1797061426066489344 |
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| author | Qian, Z Yao, Y |
| author_facet | Qian, Z Yao, Y |
| author_sort | Qian, Z |
| collection | OXFORD |
| description | We study a class of McKean–Vlasov type stochastic differential equations (SDEs) which arise from the random vortex dynamics and other physics models. By introducing a new approach we resolve the existence and uniqueness of both the weak and strong solutions for the McKean–Vlasov stochastic differential equations whose coefficients are defined in terms of singular integral kernels such as the Biot–Savart kernel. These SDEs which involve the distributions of solutions are in general not Lipschitz continuous with respect to the usual distances on the space of distributions such as the Wasserstein distance. Therefore there is an obstacle in adapting the ordinary SDE method for the study of this class of SDEs, and the conventional methods seem not appropriate for dealing with such distributional SDEs which appear in applications such as fluid mechanics.
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| first_indexed | 2024-03-06T20:30:59Z |
| format | Journal article |
| id | oxford-uuid:3105e079-6488-4c0e-9463-b8313e58fe91 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:30:59Z |
| publishDate | 2021 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:3105e079-6488-4c0e-9463-b8313e58fe912022-03-26T13:05:17ZMcKean–Vlasov type stochastic differential equations arising from the random vortex method Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3105e079-6488-4c0e-9463-b8313e58fe91EnglishSymplectic ElementsSpringer2021Qian, ZYao, YWe study a class of McKean–Vlasov type stochastic differential equations (SDEs) which arise from the random vortex dynamics and other physics models. By introducing a new approach we resolve the existence and uniqueness of both the weak and strong solutions for the McKean–Vlasov stochastic differential equations whose coefficients are defined in terms of singular integral kernels such as the Biot–Savart kernel. These SDEs which involve the distributions of solutions are in general not Lipschitz continuous with respect to the usual distances on the space of distributions such as the Wasserstein distance. Therefore there is an obstacle in adapting the ordinary SDE method for the study of this class of SDEs, and the conventional methods seem not appropriate for dealing with such distributional SDEs which appear in applications such as fluid mechanics. |
| spellingShingle | Qian, Z Yao, Y McKean–Vlasov type stochastic differential equations arising from the random vortex method |
| title | McKean–Vlasov type stochastic differential equations arising from the random vortex method
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| title_full | McKean–Vlasov type stochastic differential equations arising from the random vortex method
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| title_fullStr | McKean–Vlasov type stochastic differential equations arising from the random vortex method
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| title_full_unstemmed | McKean–Vlasov type stochastic differential equations arising from the random vortex method
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| title_short | McKean–Vlasov type stochastic differential equations arising from the random vortex method
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| title_sort | mckean vlasov type stochastic differential equations arising from the random vortex method |
| work_keys_str_mv | AT qianz mckeanvlasovtypestochasticdifferentialequationsarisingfromtherandomvortexmethod AT yaoy mckeanvlasovtypestochasticdifferentialequationsarisingfromtherandomvortexmethod |