Asymptotic behavior for sums of non-identically distributed random variables

作     者：YU Chang-jun CHENG Dong-ya 

作者机构：School of Sciences Nantong University School of Mathematical Sciences Soochow University The Statistics and Operations Research Department the University of North Carolina at Chapel Hill 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2019年第34卷第1期

页      面：45-54页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by the National Natural Science Foundation of China(no.11401415) Tian Yuan Foundation(nos.11226208 and 11426139) Natural Science Foundation of the Jiangsu Higher Education Institutions of China(no.13KJB110025) Postdoctoral Research Program of Jiangsu Province of China(no.1402111C) Jiangsu Overseas Research and Training Program for Prominent University Young and Middle-aged Teachers and Presidents 

主　　题：lower limits upper limits heavy-tailed distributions local distributions densities 

摘      要：For any given positive integer m, let X_i, 1 ≤ i ≤ m be m independent random variables with distributions F_i, 1 ≤ i ≤ m. When all the summands are nonnegative and at least one of them is heavy-tailed, we prove that the lower limit of the ratio ■equals 1 as x →∞. When the summands are real-valued, we also obtain some asymptotic results for the tail probability of the sums. Besides, a local version as well as a density version of the above results is also presented.