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

2025/07/19 by Cheng, Lingyan, Gu, Caihong, Liu, Wei +1
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2507.14546

Abstract

In this paper, we first establish the existence and uniqueness of strong solutions for multivalued McKean-Vlasov stochastic differential equations (MMVSDEs) driven by Lévy 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.

Citations

• A note on Lévy-driven McKean-Vlasov SDEs under monotonicity
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• Distribution dependent SDEs with singular coefficients
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• Support theorem for stochastic variational inequalities
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