CS37: Recent progresses on McKean-Vlasov equations and mean field interacting particle systems

Organizer: Wei Liu (Wuhan University)

Strong solution and Large deviation principles for the Multi-valued McKean-Vlasov SDEs with jumps

Lingyan Cheng

In this talk, we present a comprehensive analysis of multi-valued McKean-Vlasov stochastic differential equations (MMVSDEs) driven by Lévy noise under non-Lipschitz coefficients. Firstly, we rigorously establish the existence and uniqueness of strong solutions for this class of equations, overcoming challenges posed by the interplay between multi-valued operators, measure-dependent coefficients, and discontinuous Lévy processes. Subsequently, we investigate the asymptotic behavior of small perturbations for the system. Utilizing the weak convergence approach, we derive Freidlin-Wentzell type large deviation principles (LDPs) and moderate deviation principles (MDPs) for MMVSDEs. This talk based on the joint work with Caihong Gu, Wei Liu, and Fengwu Zhu.

Recent results on mean field interacting particle systems and McKean-Vlasov equations

Wei Liu

In this talk, we will present our recent studies about the long time behaviors of mean-field interacting particle systems and the McKean-Vlasov equation, by using two different methods: coupling method and functional inequalities. This talk is based on the joint works with Arnaud Guillin, Liming Wu, Chaoen Zhang, et al..