Le, Anh Dung and Villeneuve, Stéphane (2026) Well-Posedness of McKean-Vlasov SDEs with Density-Dependent Drift. Stochastics and Dynamics (sd ). (In Press)

Preview

Text Download (584kB) | Preview

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 Wp. 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.