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活动&公告
活动&公告
报告题目： Log-Sobolev Inequalities and Exponential Ergodicity for McKean-Vlasov SDEs
报告时间： 2026-10-16 13:00——2026-10-16 15:00
报告人： 黄兴
报告地点： 腾讯会议146 343 107
主办单位： 数据科学与人工智能学院
报告摘要：
The exponential ergodicity of partially dissipative McKean-Vlasov SDEs in the L^1-Wasserstein distance has been extensively studied using asymptotic reflection coupling. However, the reflection coupling method is not applicable for the exponential ergodicity in L^2-Wasserstein distance and relative entropy. In this paper, we first establish uniform log-Sobolev inequalities (in the frozen measure variable with bounded second moments) for the invariant probability measure of the corresponding SDEs with frozen distribution. Second, for the McKean-Vlasov SDEs, we combine the log-Harnack inequality and Talagrand's inequality to derive exponential ergodicity in both L^2-Wasserstein distance and relative entropy. Furthermore, we extend these main results to the case of degenerate diffusion.
报告人简介：
黄兴，博士毕业于北京师范大学概率论与数理统计专业，现为天津大学应用数学中心副教授。主持国家自然科学基金青年和面上项目，参与国家重点研发计划和自然科学基金重点项目。主要关注分布依赖的随机微分方程的遍历性，泛函不等式如对数Harnack不等式，（weak）Poincare不等式，log-Sobolev不等式以及平均场粒子系统的定量混沌传播。主要成果发表于Math.Ann.，JFA, AAP，nonlinearity，SPA，Bernoulli，EJP，JDE, Potential Anal.等期刊。
