Path-Distribution Dependent SDEs with Singular Coefficients

TL;DR

This paper establishes existence, uniqueness, and gradient estimates for path-dependent McKean-Vlasov SDEs with singular coefficients, extending classical results to more general, path-dependent cases with Dini continuity.

Contribution

It introduces new existence and uniqueness results for path-dependent McKean-Vlasov SDEs with singular coefficients and derives gradient estimates and Harnack inequalities under Dini continuity.

Findings

Proved existence and uniqueness for the class of SDEs.

Derived gradient estimates and Harnack inequalities.

Extended classical results to path-dependent and singular coefficient cases.

Abstract

In this paper, existence and uniqueness are proved for path-dependent McKean-Vlasov type SDEs with integrability conditions. Gradient estimates and Harnack type inequalities are derived in the case that the coefficients are Dini continuous in the space variable. These generalize the corresponding results derived for classical functional SDEs with singular coefficients.