On the density of singular SDEs with fractional noise and applications to McKean-Vlasov equations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913892361306112 |
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| author | Anzeletti, Lukas Galeati, Lucio Richard, Alexandre Tanré, Etienne |
| author_facet | Anzeletti, Lukas Galeati, Lucio Richard, Alexandre Tanré, Etienne |
| contents | We investigate properties of the (conditional) law of the solution to SDEs driven by fractional Brownian noise with a singular, possibly distributional, drift. Our results on the law are twofold: i) we quantify the spatial regularity of the law, while keeping track of integrability in time, and ii) we prove that it has a density with Gaussian tails. Then the former result is used to establish novel results on existence and uniqueness of solutions to McKean-Vlasov equations of convolutional type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the density of singular SDEs with fractional noise and applications to McKean-Vlasov equations Anzeletti, Lukas Galeati, Lucio Richard, Alexandre Tanré, Etienne Probability 60H50, 60H10, 60G22, 34A06 We investigate properties of the (conditional) law of the solution to SDEs driven by fractional Brownian noise with a singular, possibly distributional, drift. Our results on the law are twofold: i) we quantify the spatial regularity of the law, while keeping track of integrability in time, and ii) we prove that it has a density with Gaussian tails. Then the former result is used to establish novel results on existence and uniqueness of solutions to McKean-Vlasov equations of convolutional type. |
| title | On the density of singular SDEs with fractional noise and applications to McKean-Vlasov equations |
| topic | Probability 60H50, 60H10, 60G22, 34A06 |
| url | https://arxiv.org/abs/2506.11900 |