On well-posedness of stable-driven McKean-Vlasov stochastic differential equations with Besov interaction kernel of non-positive regularity
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915562783768576 |
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| author | Bahrii, Anna |
| author_facet | Bahrii, Anna |
| contents | We prove well-posedness results for time-inhomogeneous stable-driven McKean-Vlasov stochastic differential equations with a convolution drift where the interaction kernel belongs to some Lebesgue-Besov space. The novelty of this work is that we manage to go below -1 in space regularity for such a kernel. This is achieved under additional smoothness conditions on the initial data and divergence conditions on the kernel. The proof heavily relies on a suitable product rule in Besov space. We prove smoothing properties of the law, which allow us to have the drift in a Lebesgue-Besov space of non-positive regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16452 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On well-posedness of stable-driven McKean-Vlasov stochastic differential equations with Besov interaction kernel of non-positive regularity Bahrii, Anna Probability 60H10, 60H50, 35Q84, 30H25, 60G52 We prove well-posedness results for time-inhomogeneous stable-driven McKean-Vlasov stochastic differential equations with a convolution drift where the interaction kernel belongs to some Lebesgue-Besov space. The novelty of this work is that we manage to go below -1 in space regularity for such a kernel. This is achieved under additional smoothness conditions on the initial data and divergence conditions on the kernel. The proof heavily relies on a suitable product rule in Besov space. We prove smoothing properties of the law, which allow us to have the drift in a Lebesgue-Besov space of non-positive regularity. |
| title | On well-posedness of stable-driven McKean-Vlasov stochastic differential equations with Besov interaction kernel of non-positive regularity |
| topic | Probability 60H10, 60H50, 35Q84, 30H25, 60G52 |
| url | https://arxiv.org/abs/2510.16452 |