题目：Strict Kantorovich contractions for Markov chains

报告人：王健

时间：11月23日15：00-17：00

腾讯会议：168 458 034

个人简介：王健，福建师范大学教授，博士生导师，2015年获批国家优秀青年科学基金项目。2001年本科毕业于福建师范大学数学系，同年留校工作；2004年在福建师范大学获得硕士学位；2005年9月考入北京师范大学，师从中国科学院院士、北京师范大学陈木法教授，2008年6月获得理学博士学位。2009获得德国洪堡基金，2014年获得日本学术振兴基金，2015年获得国家自然科学基金优秀青年基金，同年也获得霍英东教育基金会高等院校青年教师基金。研究兴趣：随机分析。在《Adv. Math.》，《Comm. Math. Phys.》，《Annal. Appl. Prob》、《J. Funct. Anal.》等国际权威杂志上发表论文80余篇。

报告摘要：We study contractions of Markov chains on general metric spaces with respect to some carefully designed distance-like functions, which are comparable to the total variation and the standard

-Wasserstein distances for p ≥ 1. We present explicit lower bounds of the corresponding contraction rates. By employing the refined basic coupling and the coupling by reflection, the results are applied to Markov chains whose transitions include additive stochastic noises that are not necessarily isotropic. This can be useful in the study of Euler schemes for SDEs driven by Levy noises. In particular, motivated by recent works on the use of heavy tailed processes in Markov Chain Monte Carlo, we show that chains driven by the α-stable noise can have better contraction rates than corresponding chains driven by the Gaussian noise, due to the heavy tails of the α-stable distribution.