RATE OF CONVERGENCE AND EXPANSION OF RNYI ENTROPIC CENTRAL LIMIT THEOREM  

作　　者：孙建强 丁义明 

机构地区：[1]Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences [2]University of Chinese Academy of Sciences [3]National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences

出　　处：《Acta Mathematica Scientia》2015年第1期79-88,共10页数学物理学报（B辑英文版）

基　　金：supported by National Basic Research Program of China(973 Program)(2011CB707802,2013CB910200);Natural Science Foundation of China Grant(11126180)

摘　　要：We obtain the expansion of Renyi divergence of order α （0 〈 α 〈 1） between the normalized sum of IID continuous random variables and the Caussian limit under minimal moment conditions via Edgeworth-type expansion. The rate is faster than that of Shannon case, which can be used to improve the rate of convergence in total variance norm.We obtain the expansion of Renyi divergence of order α （0 〈 α 〈 1） between the normalized sum of IID continuous random variables and the Caussian limit under minimal moment conditions via Edgeworth-type expansion. The rate is faster than that of Shannon case, which can be used to improve the rate of convergence in total variance norm.

关 键 词：Renyi divergence central limit theorem Edgeworth-type expansion rate ofconvergence 

分 类 号：O211.4[理学—概率论与数理统计] O212.1[理学—数学]