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9月18日学术报告Asymptotic Log-Harnack Inequality and Ergodicity for Path-Dependent SDEs

作者:admin 点击:135 发布时间:2017-9-13 9:30:34

题目:Asymptotic Log-Harnack Inequality and Ergodicity for 
      Path-Dependent SDEs
 
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). 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. 
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:鲍建海副教授
时间与地点2017年9月18日周一  16:00-17:00  理学院547报告厅
鲍建海副教授
现为中南大学数学与统计学院副教授,2004年07月毕业于曲阜师范大学数学院的
应用数学专业,获学士学位;2007年3月毕业于中南大学数学与统计学院的概率论
与数理统计专业,获硕士学位;2013年01月毕业于英国斯旺西大学(Swansea 
University)的概率论与数理统计专业,获博士学位;2012年09月---2013年08月
在美国韦恩州立大学(Wayne State University) 从事 Research Fellow,2017年
01月---2019年12月在英国Swansea 大学做research fellow, 先后在Stoch.Proc.
Appl.,Bernoulli, Electron. J. Probab.,J. Theoret. Probab.,Potential Anal.,
SIAM J. Control Optim.,SIAM J. Appl. Math. 等期刊上发表多篇篇学术论文。
 
 
  联系人:蒋辉