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 (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.

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..