Killed path-dependent McKean-Vlasov SDEs for a probabilistic representation of non-conservative McKean PDEs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916872829534208 |
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| author | Morale, Daniela Tarquini, Leonardo Ugolini, Stefania |
| author_facet | Morale, Daniela Tarquini, Leonardo Ugolini, Stefania |
| contents | A McKean-Vlasov stochastic differential equation subject to killing associated to a regularised non-conservative and path-dependent nonlinear parabolic partial differential equation is studied. The existence and pathwise uniqueness of a strong solution and the regularity properties of its sub-probability law are proved. The density of such a law may be seen as a weak solution of the considered PDE. The well-posedness of the associated particle system is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Killed path-dependent McKean-Vlasov SDEs for a probabilistic representation of non-conservative McKean PDEs Morale, Daniela Tarquini, Leonardo Ugolini, Stefania Probability 60H10, 60H30, 60K35, 60J60, 60J75, 60J85, 82C22, 82C31 A McKean-Vlasov stochastic differential equation subject to killing associated to a regularised non-conservative and path-dependent nonlinear parabolic partial differential equation is studied. The existence and pathwise uniqueness of a strong solution and the regularity properties of its sub-probability law are proved. The density of such a law may be seen as a weak solution of the considered PDE. The well-posedness of the associated particle system is also discussed. |
| title | Killed path-dependent McKean-Vlasov SDEs for a probabilistic representation of non-conservative McKean PDEs |
| topic | Probability 60H10, 60H30, 60K35, 60J60, 60J75, 60J85, 82C22, 82C31 |
| url | https://arxiv.org/abs/2507.23353 |