Well-posedness of McKean-Vlasov SDEs with density-dependent drift
Probability
2025-11-20 v3
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 . Our approach is by approximation with mollifiers. We prove strong existence of a solution. Weak and strong uniqueness are obtained when , the drift coefficient is bounded, and the diffusion coefficient is distribution free.
Keywords
Cite
@article{arxiv.2404.19499,
title = {Well-posedness of McKean-Vlasov SDEs with density-dependent drift},
author = {Anh-Dung Le and Stéphane Villeneuve},
journal= {arXiv preprint arXiv:2404.19499},
year = {2025}
}