Precise asymptotics in Chung's law of the iterated logarithm

被引：2
|
作者：
Zhang, Li Xin [1 ]
机构：
[1] Zhejiang Univ, Dept Matemat, Hangzhou 310027, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2008年 / 24卷 / 04期
基金：
中国国家自然科学基金;
关键词：
the law of the iterated logarithm; Chung's law of the iterated logarithm; small deviation; i.i.d; random variables;
D O I：
10.1007/s10114-007-1033-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let X, X-1, X-2,... be i.i.d. random variables with mean zero and positive, finite variance sigma(2), and set S-n = X1 +... + Xn, n = 1. The author proves that, if EX 2 I{vertical bar X vertical bar = t} = o(( log log t)(-1)) as t -> 8, then for any a > -1 and b > -1, [GRAPHICS] whenever a(n) = o( 1/log log n). The author obtains the sufficient and necessary conditions for this kind of results to hold.
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页码：631 / 646
页数：16
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