Uniform Estimate for The Tail Probabilities of Randomly Weighted Sums  

作　　者：Yin-feng WANG Chuan-cun YIN Xin-sheng ZHANG 

机构地区：[1]Department of Statistics,Fudan University [2]School of Business,Shanghai Dianji University [3]School of Mathematical Sciences,Qufu Normal University

出　　处：《Acta Mathematicae Applicatae Sinica》2014年第4期1063-1072,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11071045,No.11171179,No.11201080,No.11301391);the Research Fund for the Doctoral Program of Higher Education of China(No.20133705110002)

摘　　要：Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sumsa.ud their maxima. In this paper, we generalize their work to the situation thatis a sequence of upper tail asymptotically independent random variables with common distribution from the is a sequence of nonnegative random variables, independent of and satisfying some regular conditions. Moreover. no additional assumption is required on the dependence structureof {θi,i≥ 1）.Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sumsa.ud their maxima. In this paper, we generalize their work to the situation thatis a sequence of upper tail asymptotically independent random variables with common distribution from the is a sequence of nonnegative random variables, independent of and satisfying some regular conditions. Moreover. no additional assumption is required on the dependence structureof {θi,i≥ 1）.

关 键 词：uniform estimate randomly weighted sums upper tail asymptotically independence class D ∩ζ 

分 类 号：O212.1[理学—概率论与数理统计]