Regularities and Exponential Ergodicity in Entropy for SDEs Driven by Distribution Dependent Noise
数学专题报告
报告题目(Title)：Regularities and Exponential Ergodicity in Entropy for SDEs Driven by Distribution Dependent Noise
报告人(Speaker)：黄兴 (天津大学)
地点(Place)：后主楼1124
时间(Time)：2024年6月18日上午11:00-12:00
邀请人(Inviter)：蒲飞
报告摘要
As two crucial tools characterizing regularity properties of stochastic systems, the log-Harnack inequality and Bismut formula have been intensively studied for distribution dependent (McKean-Vlasov) SDEs. However, due to technical difficulties, existing results mainly focus on the case with distribution free noise. In this paper, we introduce a noise decomposition argument to establish the log-Harnack inequality and Bismut formula for SDEs with distribution dependent noise, in both non-degenerate and degenerate situations. As application, the exponential ergodicity in entropy is investigated.
