The locally homeomorphic property and the multiplicative ergodic theorem for McKean-Vlasov SDEs中国科学院数学与系统科学研究院应用数学研究所

The locally homeomorphic property and the multiplicative ergodic theorem for McKean-Vlasov SDEs

Speaker: 柳振鑫教授，大连理工大学

Inviter: 周喆

Title: The locally homeomorphic property and the multiplicative ergodic theorem for McKean-Vlasov SDEs

Language: Chinese

Time & Venue: 2024.11.08 10:00-11:00 南楼620

Abstract: In this talk, we will explore two aspects that distinguish McKean-Vlasov SDEs significantly from classical SDEs. In the first part, we establish the locally diffeomorphic property of the solution to McKean-Vlasov SDEs defined in the Euclidean space. We observe that although the coefficients are global Lipschitz, the solution in general does not satisfy the globally homeomorphic property at any time except the initial time. In the second part, we introduce the concept of Lyapunov exponents for McKean-Vlasov SDEs. We observe that even when the coefficients are regular enough and the first-order derivatives are bounded, the limit in the definition of Lyapunov exponents may not exist. Furthermore, we establish the mean-field version of the multiplicative ergodic theorem. This talk is based on the collaboration with Xianjin Cheng and Lixin Zhang.