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

被引：1
|
作者：
Fu, Ke Ang [1 ]
Huang, Wei [2 ]
机构：
[1] Zhejiang Gongshang Univ, Sch Stat & Math, Hangzhou 310018, Zhejiang, Peoples R China
[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2016年 / 32卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Domain of attraction of the normal law; geometrically weighted series; law of the iterated logarithm; self-normalization; slowly varying; RANDOM-VARIABLES; STRONG APPROXIMATION; SUMS;
D O I：
10.1007/s10114-016-4323-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let {X, X-n; n >= 0} be a sequence of independent and identically distributed random variables with EX = 0, and assume that EX2 I(vertical bar X vertical bar <= x) is slowly varying as x -> 8, 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 Sigma(infinity)(n=0) beta X-n(n) (0 < beta 1) is obtained, under some minimal conditions.
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页码：384 / 392
页数：9
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