Singular McKean-Vlasov SDEs: Well-Posedness, Regularities and Wangs Harnack Inequality

TL;DR

This paper investigates the well-posedness and regularity of singular McKean-Vlasov SDEs with complex drifts, establishing new results including Wangs Harnack inequality, applicable also to classical SDEs with distribution-independent coefficients.

Contribution

It provides novel well-posedness and regularity results for singular McKean-Vlasov SDEs and proves Wangs Harnack inequality under strengthened conditions, extending classical SDE theory.

Findings

Established well-posedness and regularity estimates for singular McKean-Vlasov SDEs.

Proved Wangs Harnack inequality when the superlinear drift term is Lipschitz continuous.

Extended results to classical Ito SDEs with distribution-independent coefficients.

Abstract

The well-posedness and regularity estimates in initial distributions are derived for singular McKean-Vlasov SDEs, where the drift contains a locally standard integrable term and a superlinear term in the spatial variable, and is Lipchitz continuous in the distribution variable with respect to a weighted variation distance. When the superlinear term is strengthened to be Lipschitz continuous, Wangs Harnack inequality is established. These results are new also for the classical Ito SDEs where the coefficients are distribution independent.