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

Lingyan Cheng; Caihong Gu; Wei Liu; Fengwu Zhu

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arXiv · 2507.14546

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

Lingyan Cheng·Caihong Gu·Wei Liu·Fengwu Zhu

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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.

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Lingyan Cheng, Caihong Gu, Wei Liu, Fengwu Zhu. 2025-07-19. Existence of Solutions for Multivalued Mckean-Vlasov SDEs with Non-Lipschitz Coefficients Driven by Jump Processes. https://arxiv.org/abs/2507.14546

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