Existence of Solutions for Multivalued Mckean-Vlasov SDEs with Non-Lipschitz Coefficients Driven by Jump Processes

TL;DR

This paper proves the existence and uniqueness of solutions for complex multivalued McKean-Vlasov SDEs driven by jump processes, extending the theory to non-Lipschitz coefficients and different solution concepts.

Contribution

It establishes the existence and uniqueness of strong solutions under non-Lipschitz conditions and explores weak and martingale solutions for these equations.

Findings

Proved strong solution existence and uniqueness for multivalued McKean-Vlasov SDEs with jumps.

Established weak solution existence under linear growth conditions.

Demonstrated the existence of martingale solutions.

Abstract

In this paper, we first establish the existence and uniqueness of strong solutions for multivalued McKean-Vlasov stochastic differential equations (MMVSDEs) driven by L\'evy noise with non-Lipschitz coefficients. It is important to note that these findings are based upon the well-posedness of strong solutions for MMVSDEs under Lipschitz conditions, which will be stated briefly. Secondly, we study the existence of weak solutions under linear growth condition. Finally, we prove the existence of martingale solutions.