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The locally homeomorphic property and the multiplicative ergodic theorem for McKean-Vlasov SDEs
- 来源：
- 学校官网
- 收录时间：
- 2025-10-18 15:46:06
- 时间：
- 2025-09-19 10:00:00
- 地点：
- 二号学院楼2432报告厅
- 报告人：
- 柳振鑫
- 学校：
- -/-
- 关键词：
- McKean-Vlasov SDEs, locally homeomorphic property, multiplicative ergodic theorem, Lyapunov exponents, mean-field
- 简介：
- 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.
- -/- 14
报告介绍：
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.
报告人介绍：
柳振鑫，大连理工大学数学科学学院教授、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、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；2025年获国家自然科学基金重点项目资助。
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