中南大学概率统计及相关领域学术论坛

发布时间:2017年07月12日 作者:唐颖   消息来源:业务办    阅读次数:[]

时间:2017年7月15日 上午(上午8点开始)和下午

地点:数理楼一楼小报告厅 (概率方面的报告)

Title 1: Markov processes with darning and their approximations

Speaker: Zhenqing Chen, University of Washington

陈振庆教授现为美国华盛顿大学(西雅图)(University of Washington, Seattle)数学系教授,2007 年受聘为北京理工大学“长江学者奖励计划讲座教授”,2017年受聘为北京理工大学国家“千人计划”特聘专家。陈振庆教授主要从事马氏过程与随机分等方面研究,在马氏过程与狄氏空间,随机微分方程以及偏微分方程中的概率论方法等方面做了大量开创性的研究工作。 ?陈振庆教授在《Ann. Probab.》,《Probab. Theory Related Fields》, 《Stochastic Process. Appl.》, 《J. Funct. Anal. 》, 《Potential Anal.》 等国际权威杂志上发表论文150多篇,出版了专著1部。 目前为国际权威期刊《Potential Analysis》的主编,《Annals of Probability》副主编。

Abstract: This talk is concerned with? darning of general symmetric Markov processes by shorting some parts of the state space into singletons. We will present a natural way to construct such processes? by using a Dirichlet form approach. When the initial processes have discontinuous sample paths, the processes constructed in this way are the genuine? extensions of those studied in Chen and Fukushima (2012). We further show that, up to a time change, these Markov processes with darning can be approximated in the finite dimensional sense? by introducing additional large intensity jumps among these compact sets to be collapsed into singletons to the original Markov processes. For diffusion processes, it is also possible to get, up to a time change, diffusions with darning by increasing the conductance on these compact sets to infinity. To accomplish these, we extend the semigroup characterization of Mosco convergence to closed symmetric forms whose domain of definition may not be dense in the $L^2$-space. The latter is of independent interest and potentially useful in the study of convergence of Markov processes having different state spaces.? Based on joint work with Jun Peng.


Title 2: Distances between Random Orthogonal Matrices and Independent Normals

Speaker: Tiefeng Jiang, University of Minnesota

姜铁锋教授现为美国明尼苏达大学统计学院的教授,主要从事概率统计理论及其相关领域的研究,特别是在概率论、高维统计学以及纯数学等交叉学科取得了突破性的进展和开创性的成果。姜教授除获得多次美国自然科学基金外,还获得2005年的美国总统奖。姜教授目前已发表论文30多篇,其中绝大部分发表在国际顶尖的概率统计与机器学习杂志上,包括《Ann. Probab.》5篇,《Probab. Theor. Rel. Fields》3篇,《Ann. Stat.》2篇,《Ann. Appl. Probab.》2篇,《Journal of Machine Learning Research》1篇等等。 Abstract: We study the distance between Haar-orthogonal matrices and independent normal random variables. The distance is measured by the total variation distance, the Kullback-Leibler distance, the Hellinger distance and the Euclidean distance. They appear different features. Optimal rates are obtained. This is a joint work with Yutao Ma.?

Title 3: Regularity of different type of noises to the deterministic system ?

Speaker: 谢颖超,江苏师范大学 谢颖超教授为江苏师范大学数学与统计学院教授,南开大学数学科学学院博士生导师。荣获中华人民共和国政府特殊津贴、全国模范教师、江苏高校优势学科“统计学”学科带头人、江苏省科学技术进步奖三等奖等多项荣誉和奖项。谢教授主要从事随机分析及其应用、随机偏微分方程、随机过程极限定理等方面的研究工作,取得了一系列重要的研究成果,谢教授在《Stochastic Process Appl.》、《Stochastic Anal. Appl.》、《中国科学》等国内外一流刊物上发表学术论文60余篇,连续多次获得国家自然科学基金面上项目资助。

We show the existence and uniqueness of strong solutions for stochastic differential equation driven by partial? $\alpha$-stable noise and partial Brownian noise with singular coefficients. The proof is based on the regularity?of degenerate mixed type Kolmogorov equation. Based on joint work with Yueling Li and Longjie Xie.

Title 4: The Censored Markov Chain and the Best Augmentation

Speaker: Yiqiang Q. Zhao, Carleton Unviersity Abstract: Computationally, when we solve for the stationary probabilities for a countable-state Markov chain, the transition probability matrix of the Markov chain has to be truncated, in some way, into a finite one. Various augmentation methods might be valid such that the stationary probability distribution for the truncated Markov chain approaches that for the countable Markov chain as the truncation size gets large. In this talk, we introduce the censored Markov chain, one of the truncation method, and prove that the censored (watched) Markov chain provides the best approximation in the sense that for a given truncation size the sum of errors is the minimum and show, by examples, that the method of augmenting the last column only is not always the best.

赵以强教授现为加拿大卡尔顿大学数学与统计学院教授,卡尔顿大学科学院副院长(主管研究生)。他在应用概率和排队论领域做出了一系列开创性的研究工作,在国际同行里享有很高的声誉,他在国际一流的学术刊物《Advances in Applied Probability》、《 Journal of Applied Probability》、《Queueing System》、《IEEE Transactions on Networking》上发表100余篇学术论文。现为《Queueing Systems》、《Operation Research Letters》、《Stochastic Models》、《Advances in Operations Research》等期刊的编委。



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