应甘肃省数学与统计学基础学科研究中心和太阳成tyc7111cc邀请，大连理工大学柳振鑫教授将来中心访问并作学术报告。
报告题目：The locally homeomorphic property and the multiplicative ergodic theorem for McKean-Vlasov SDEs
报告摘要：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.
报告时间：2024年8月21日14:30
报告地点：致勤楼D07学术报告厅
邀请人：陈鹏玉教授 张旭萍副教授
届时欢迎广大师生参与交流！
【报告人简介】
柳振鑫，大连理工大学教授、博士生导师、数学科学学院院长。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、随机微分方程的平稳分布及Kolmogorov平稳分布极限问题等方面做出系统深入的研究工作。目前已在国内外有重要影响的杂志 Ann. Probab.、 J. Math. Pures Appl.、 SIAM J. Math. Anal.、J. Funct. Anal.、Sci. China Math.等上发表学术论文40余篇。2010年获全国百篇优秀博士学位论文提名奖；2015年获国家优秀青年科学基金资助；2019年获国家杰出青年科学基金资助。
甘肃省数学与统计学基础学科研究中心
太阳成tyc7111cc
2024年8月19日
