学术报告
报告人：鲍建海
报告题目：Asymptotic Log-Harnack Inequality and Ergodicity for Path-Dependent SDEs with Infinite Memory
时间：2017-09-14 (星期四) 15:00 ~ 16:00
地点：数学研究中心学术报告厅
主办：数学与信息学院
参加对象：概率统计方向老师和研究生
报告摘要：The (log-) Harnack inequality and the gradient estimate for path-dependent SDEs have been extensively investigated, where the length of memory is finite and the diffusion terms depend only on the present state. In this paper, 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).Asanother 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. Moreover, via weak Harris' theorem, we discuss the exponential ergodicity under the Wasserstein distance for a wide class of path-dependent SDEs with infinite memory.
报告人简介：鲍建海，博士，2004年本科毕业于曲阜师范大学，2007年硕士研究生毕业于中南大学，2013年博士毕业于英国斯旺西大学 (Swansea University), 目前任职于中南大学数学与统计学院，主要从事泛函随机微分方程以及马氏切换过程等研究，鲍建海博士曾在《Stochastic Process. Appl》、《Bernoulli》、《Electron. J. Probab.》、《J. Theoret. Probab.》、《J. Appl. Probab.》、《 Potential Analysis》、《SIAM J. Control Optim.》，《SIAM J. Appl. Math.》等期刊上发表多篇学术论文上.
