Well-posedness of McKean-Vlasov SDEs with density-dependent drift

Anh-Dung Le; Stéphane Villeneuve

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arXiv · 2404.19499

Well-posedness of McKean-Vlasov SDEs with density-dependent drift

Anh-Dung Le·Stéphane Villeneuve

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Abstract

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.

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BibTeX RIS

Anh-Dung Le, Stéphane Villeneuve. 2024-04-30. Well-posedness of McKean-Vlasov SDEs with density-dependent drift. https://arxiv.org/abs/2404.19499

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