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

date: 7/14/2025, time: 14:00-15:30, room: IM 605

Organizer: WEI LIU (WUHAN UNIVERSITY)

Chair: WEI LIU (WUHAN UNIVERSITY)

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

Wei Liu (Wuhan University)

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..

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

Lingyan Cheng (Nanjing University of Science and Technology)

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.

A large deviation principle for nonlinear stochastic wave equation driven by rough noise

Ruinan Li (Shanghai University of International Business and Economics)

In this talk, we focus on the Freidlin-Wentzell’s large deviation principle for one dimensional nonlinear stochastic wave equation driven by a Gaussian noise which is white in time and fractional in space with Hurst parameter \(1/4<H<1/2\). The variational framework and the modified weak convergence criterion proposed by Matoussi, Sabbagh, Zhang (2021) are adopted here.