A Self-normalized Law of the Iterated Logarithm for the Geometrically Weighted Random Series  

作　　者：Ke Ang FU Wei HUANG 

机构地区：[1]School of Statistics and Mathematics,Zhejiang Gongshang University [2]Department of Mathematics,Zhejiang University

出　　处：《Acta Mathematica Sinica,English Series》2016年第3期384-392,共9页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11301481,11371321 and 10901138);National Statistical Science Research Project of China(Grant No.2012LY174);Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ12A01018);the Fundamental Research Funds for the Central Universities and Zhejiang Provincial Key Research Base for Humanities and Social Science Research(Statistics)

摘　　要：Let {X, Xn; n ≥ 0} be a sequence of independent and identically distributed random variables with EX=0, and assume that EX^2I（｜X｜ ≤ x） is slowly varying as x →∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series Σ~∞（n=0）β~nXn（0 〈 β 〈 1） is obtained, under some minimal conditions.Let {X, Xn; n ≥ 0} be a sequence of independent and identically distributed random variables with EX=0, and assume that EX^2I（｜X｜ ≤ x） is slowly varying as x →∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series Σ~∞（n=0）β~nXn（0 〈 β 〈 1） is obtained, under some minimal conditions.

关 键 词：Domain of attraction of the normal law geometrically weighted series law of the iteratedlogarithm SELF-NORMALIZATION slowly varying 

分 类 号：O211.5[理学—概率论与数理统计]