学 术 报 告

报告题目：An Excess Entropy Characterization of Long Memory for Stationary Gaussian Process

报告人： 向绪言 教授

报告时间：2020年9月15日 16:00-17:00

地点： 数统院307

数学与统计学院

2020.9.15

报告摘要： Long memory or long range dependency is an important phenomenon that may arise in the analysis of time series or spatial data. Most of the definitions of long memory of a stationary process X = {X1,X2,…,} are based on the second-order properties of the process. The excess entropy of a stationary process is the summation of redundancies which relates to the rate of convergence of the conditional entropy H(Xn|Xn-1,…,X1) to the entropy rate. And its excess entropy is identical to the mutual information between the past and the future when the entropy H(X1) is finite. We suggest a new definition that a stationary process is long memory if the excess entropy is infinite. Since the definition of excess entropy of a stationary process requires very weak moment condition on the distribution of the process, it can be applied to processes whose distributions without bounded second moment. The most significant property of excess entropy is that it is invariant under invertible transformation, which enables us to know the excess entropy of a stationary process from the excess entropy of other process. For stationary Guassian process, the excess entropy characterization of long memory relates to popular characterization well.

报告人简介：向绪言，博士，教授，硕士生导师，湖南文理学院教师工作部部长、人事处处长，原数学与计算科学学院院长；湖南省新世纪“121人才工程”人选；中国工程概率统计学会常务理事，湖南省数学会常务理事。主要从事随机过程统计、计算及应用（生物信息、神经网络、随机计算与智能系统）方向的科研工作，发表论文40余篇。主持国家自然科学基金（面上项目）、教育部留学回国人员科研启动基金、湖南省自然科学基金等科研课题10余项，参与国家自然科学基金等10多项。