報告人：柳振鑫 大連理工大學數學科學學院 教授

主持人：張曉穎

時 間：3月30日 下午14:30

地 點：#騰訊會議：694-996-864

主辦單位：長春大學 數學與統計學院

報告人簡介：柳振鑫，大連理工大學數學科學學院教授。主要從事隨機動力系統的研究，在隨機Conley指標理論、隨機動力系統中的回復性和穩定性、Kolmogorov平穩分布極限問題、隨機平均原理等方面做出系統深入的研究工作。目前已發表學術論文40余篇。2010年獲全國百篇優秀博士學位論文提名獎；2015年獲得國家優秀青年科學基金資助；2019年獲得國家杰出青年科學基金資助。 

觀點綜述：In this report, 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.