Mckean-vlasov sdes with drifts discontinuous under wasserstein distance

Abstract

Existence and uniqueness are proved for McKean-Vlasov type distribution dependent SDEs with singular drifts satisfying an integrability condition in space variable and the Lipschitz condition in distribution variable with respect to W0 or W0 + Wθ for some θ ≥ 1, where W0 is the total variation distance and Wθ is the Lθ-Wasserstein distance. This improves some existing results (see for instance [13]) derived for drifts continuous in the distribution variable with respect to the Wasserstein distance.