Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910479130034176 |
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| author | Jarni, Imane Missaoui, Badr Ouknine, Youssef |
| author_facet | Jarni, Imane Missaoui, Badr Ouknine, Youssef |
| contents | In this paper, we investigate the deterministic multidimensional Skorokhod problem with normal reflection in a family of time-dependent convex domains that are càdlàg with respect to the Hausdorff metric. We then show the existence and uniqueness of solutions to multidimensional McKean-Vlasov stochastic differential equations reflected in these time-dependent domains. Additionally, we derive stability properties with respect to the initial condition and the coefficients. Finally, we establish a propagation of chaos result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05807 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains Jarni, Imane Missaoui, Badr Ouknine, Youssef Probability In this paper, we investigate the deterministic multidimensional Skorokhod problem with normal reflection in a family of time-dependent convex domains that are càdlàg with respect to the Hausdorff metric. We then show the existence and uniqueness of solutions to multidimensional McKean-Vlasov stochastic differential equations reflected in these time-dependent domains. Additionally, we derive stability properties with respect to the initial condition and the coefficients. Finally, we establish a propagation of chaos result. |
| title | Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains |
| topic | Probability |
| url | https://arxiv.org/abs/2406.05807 |