Multidimensional Stable Driven McKean-Vlasov SDEs with Distributional Interaction Kernel: Critical Thresholds and Related Models
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911067243806720 |
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| author | de Raynal, P. -E Chaudru Jabir, J. -F Menozzi, S |
| author_facet | de Raynal, P. -E Chaudru Jabir, J. -F Menozzi, S |
| contents | In this work we continue to investigate well-posedness for stable driven McKean-Vlasov SDEs with distributional interaction kernel following the approach introduced in [8]. We specifically focus on the impact of the Besov smoothness of the initial condition and quantify how it affects the corresponding density estimates for the SDE. In particular, we manage to attain some critical thresholds allowing to revisit/address in a stable noise setting some concrete physical and biological models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09900 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multidimensional Stable Driven McKean-Vlasov SDEs with Distributional Interaction Kernel: Critical Thresholds and Related Models de Raynal, P. -E Chaudru Jabir, J. -F Menozzi, S Analysis of PDEs Probability In this work we continue to investigate well-posedness for stable driven McKean-Vlasov SDEs with distributional interaction kernel following the approach introduced in [8]. We specifically focus on the impact of the Besov smoothness of the initial condition and quantify how it affects the corresponding density estimates for the SDE. In particular, we manage to attain some critical thresholds allowing to revisit/address in a stable noise setting some concrete physical and biological models. |
| title | Multidimensional Stable Driven McKean-Vlasov SDEs with Distributional Interaction Kernel: Critical Thresholds and Related Models |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2302.09900 |