报告人：柳振鑫 大连理工大学数学科学学院 教授

主持人：张晓颖

时 间：3月30日 下午14:30

地 点：#腾讯会议：694-996-864

主办单位：长春大学 数学与统计学院

报告人简介：柳振鑫，大连理工大学数学科学学院教授。主要从事随机动力系统的研究，在随机Conley指标理论、随机动力系统中的回复性和稳定性、Kolmogorov平稳分布极限问题、随机平均原理等方面做出系统深入的研究工作。目前已发表学术论文40余篇。2010年获全国百篇优秀博士学位论文提名奖；2015年获得国家优秀青年科学基金资助；2019年获得国家杰出青年科学基金资助。 

观点综述：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.