报告题目：Multi-Scale McKean--Vlasov Diffusions with Super-Linear Kernels: a Lifted Semigroup Approach

报告人: 洪伟 江苏师范大学

报告时间: 6月12日 周五 下午 16:00-17:00

报告地点: 第五教学楼5107教室

摘要：

In this talk, we concern with the small-noise asymptotic behaviour (namely, the functional law of large numbers and the large/moderate deviation principle) for multi-scale McKean--Vlasov diffusions with super-linear kernels. In this setting, the interaction depends on the laws of both the slow component and the fast oscillating process. Consequently, the frozen (parameterized) system exhibits McKean--Vlasov dynamics, forming a nonlinear Markov process and thereby rendering the analysis more complex compared to existing works.

We develop a lifted semigroup argument and employ a generalized Khasminskii time discretization scheme to derive the small-noise limit of the slow variable, providing explicit convergence rates. Furthermore, we introduce the notion of a lifted viable pair and utilize a generalized functional occupation measure approach to establish the Laplace principle, which is equivalent to the large deviation principle. The main results of this work find broad applications in multi-scale models arising in fields such as machine learning and optimization theory. In particular, our results can be employed to analyze the dynamics of multi-scale consensus-based methods for multilevel optimization.