Well-posedness of McKean-Vlasov SDEs with density-dependent drift
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912717544095744 |
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| author | Le, Anh-Dung Villeneuve, Stéphane |
| author_facet | Le, Anh-Dung Villeneuve, Stéphane |
| contents | In this paper, we study well-posedness of McKean-Vlasov stochastic differential equations (SDE) whose drift depends pointwisely on marginal density and satisfies a local integrability condition in time-space variables. The drift and noise coefficients are assumed to be Lipschitz continuous in distribution variable with respect to Wasserstein metric $W_p$. Our approach is by approximation with mollifiers. We prove strong existence of a solution. Weak and strong uniqueness are obtained when $p=1$, the drift coefficient is bounded, and the diffusion coefficient is distribution free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of McKean-Vlasov SDEs with density-dependent drift Le, Anh-Dung Villeneuve, Stéphane Probability In this paper, we study well-posedness of McKean-Vlasov stochastic differential equations (SDE) whose drift depends pointwisely on marginal density and satisfies a local integrability condition in time-space variables. The drift and noise coefficients are assumed to be Lipschitz continuous in distribution variable with respect to Wasserstein metric $W_p$. Our approach is by approximation with mollifiers. We prove strong existence of a solution. Weak and strong uniqueness are obtained when $p=1$, the drift coefficient is bounded, and the diffusion coefficient is distribution free. |
| title | Well-posedness of McKean-Vlasov SDEs with density-dependent drift |
| topic | Probability |
| url | https://arxiv.org/abs/2404.19499 |