报告人：鲍建海，中南大学 

报告题目： Asymptotic log-Harnack inequality for path-dependent SDEs

时间：9月20号（周三），下午2:40-3:40

地点：管研楼1208

摘要：

In this talk, we shall establish the asymptotic log-Harnack inequality for a range of path-dependent SDEs, which allow the length of memory to be infinite and the diffusion terms to be dependent fully on the past history. We reveal that the asymptotic log-Harnack inequality implies (i) the asymptotic heat kernel estimate, (ii) the absolute continuity of the transition kernel w.r.t. the invariant probability measure and (iii) the uniqueness of invariant probability measure (if it exists). As another byproduct of the asymptotic log-Harnack inequality, we also derive the asymptotic gradient estimate, which further implies that the semigroup generated by the segment process enjoys the asymptotic strong Feller property.