学术报告：Log-Sobolev Inequality for Decoupled and McKean-Vlasov SDEs and Application on Exponential Ergodicity

报告时间：3月7日（星期五）下午15:00-16:00

报告地点：沙河校区，学院1号楼102会议室

主持人：张少钦 副教授

报告人：黄兴，天津大学，副教授

报告摘要：The exponential ergodicity in the L1-Wasserstein distance for partially dissipative McKean-Vlasov SDEs has been extensively studied. However, the question of exponential ergodicity in the L2-Wasserstein distance and relative entropy has remained unresolved. This paper addresses the problem by establishing the log-Sobolev inequality for both the time-marginal distributions and the invariant probability measure, providing a positive resolution. As part of the groundwork, the log-Sobolev inequality is investigated for the associated time-inhomogeneous semigroup. The main results are further extended to degenerate diffusion.

报告人简介：黄兴，男，2017年博士毕业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。研究方向：随机分析。先后主持国家自然科学基金青年和面上项目，参与科技部重点研发项目。主要关注分布依赖的随机微分方程的解的适定性，定量的混沌传播和分布性质如正则性估计，对数Harnack不等式和遍历性等。

撰稿人：刘洁

审稿人：邓露