Well-posedness for path-dependent multivalued McKean-Vlasov stochastic differential equations

TL;DR

This paper establishes the well-posedness of path-dependent multivalued McKean-Vlasov stochastic differential equations under both Lipschitz and non-Lipschitz conditions, advancing the theoretical understanding of such complex stochastic systems.

Contribution

It extends well-posedness results to non-Lipschitz cases for path-dependent multivalued McKean-Vlasov equations using approximation and iterative methods.

Findings

Proved well-posedness under Lipschitz conditions.

Generalized results to non-Lipschitz conditions.

Established iterative approach for distribution-dependent equations.

Abstract

This work concerns a type of path-dependent multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the well-posedness for path-dependent multivalued stochastic differential equations under the Lipschitz conditions. Then by constructing Lipschitz approximation sequences, we generalize the result to the case of the non-Lipschitz conditions. Finally, based on the obtained results, the well-posedness for path-dependent multivalued McKean-Vlasov stochastic differential equations under the non-Lipschitz conditions is established by iterating in distributions.