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 \begin{document}$ {\mathbb W}_0 $\end{document} or \begin{document}$ {\mathbb W}_0+{\mathbb W}_\theta $\end{document} for some \begin{document}$ \theta\ge 1 $\end{document} , where \begin{document}$ {\mathbb W}_0 $\end{document} is the total variation distance and \begin{document}$ {\mathbb W}_\theta $\end{document} is the \begin{document}$ L^\theta $\end{document} -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.

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