报告题目：Stability and Phase Structure of Cooperative McKean-Vlasov SDEs
时 间：2025年6月4日（星期三）15:30
地 点：科研楼18号楼1102
主 办：数学与统计学院
参加对象：概率统计系及其他感兴趣的师生
报告摘要：In this work, we present a general framework for studying McKean-Vlasov SDEs via monotone dynamical systems. Under a cooperative condition, we show McKean-Vlasov SDEs admit a comparison principle with respect to the stochastic order, and generate monotone dynamical systems on the 2-Wasserstein space. Our main results target on total orderedness of invariant measures, global convergence to order interval enclosed by two order-related invariant measures, alternating arrangement of invariant measures in terms of stability (locally attracting) and instability (connecting orbits). A wide range of classical examples are covered by our framework, such as granular media equations in double-well and multi-well confinement potentials with quadratic interaction, double-well landscapes with perturbation, and higher dimensional equations, even driven by multiplicative noises.
报告人简介：屈宝友，杜伦大学博士后（已出站）即将入职山东大学，博士毕业于山东大学。主要研究方向包括非线性期望、倒向随机微分方程、McKean-Vlasov 方程、随机动力系统等，已在《J. Differential Equations》、《Nonlinearity》、《Electron. J. Probab.》、《Stochastic Process. Appl.》等国际期刊发表数篇论文。