Precise Rates in the Generalized Law of the Iterated Logarithm in R~m

被引：2
|
作者：
Mingzhou XU [1 ]
Yunzheng DING [1 ]
Yongzheng ZHOU [1 ]
机构：
[1] School of Information and Engineering, Jingdezhen Ceramic University
来源：
Journal of Mathematical Research with Applications | 2018年 / 38卷 / 01期
基金：
中国国家自然科学基金;
关键词：
precise rates; law of iterated logarithm; complete convergence; i.i.d. random vectors;
D O I：
暂无
中图分类号：
O173 [无穷级数论（级数论）];
学科分类号：
摘要：
Let {X, Xn, n ≥ 1} be a sequence of i.i.d. random vectors with EX =（0,..., 0）m×1 and Cov（X, X） = σ2 Ⅰm, and set Sn =∑i=1n Xi, n ≥ 1. For every d > 0 and an =o(（log log n）-d), the article deals with the precise rates in the genenralized law of the iterated logarithm for a kind of weighted infinite series of P(|Sn| ≥（ε + an）σn1/2（log log n）d).
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页码：103 / 110
页数：8
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