Existence of Solutions for Multivalued Mckean-Vlasov SDEs with Non-Lipschitz Coefficients Driven by Jump Processes
Probability
2025-07-30 v3 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2507.14546,
title = {Existence of Solutions for Multivalued Mckean-Vlasov SDEs with Non-Lipschitz Coefficients Driven by Jump Processes},
author = {Lingyan Cheng and Caihong Gu and Wei Liu and Fengwu Zhu},
journal= {arXiv preprint arXiv:2507.14546},
year = {2025}
}