NA随机变量序列加权和的Chover型重对数律

数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 674-683.

NA随机变量序列加权和的Chover型重对数律

邱德华|陈平炎

广东财经大学数学与统计学院广州 510320；暨南大学数学系广州 510630

收稿日期:2012-08-07 修回日期:2013-06-02 出版日期:2014-06-25 发布日期:2014-06-25
基金资助:
国家自然科学基金(11271161)资助

Chover´s Law of Iterated Logarithm for Weighted Partial Sums of NA Random Variables Sequences

QIU De-Hua, CHEN Ping-Yan

School of Mathematics and Statistics, Guangdong University of Finance &|Economics, Guangzhou 510320； Department of Mathematics, Jinan University, Guangzhou 510630

Received:2012-08-07 Revised:2013-06-02 Online:2014-06-25 Published:2014-06-25
Supported by:
国家自然科学基金(11271161)资助

摘要/Abstract

摘要：

利用NA随机变量的指数不等式,对于具有重尾分布的同分布的NA随机变量序列,得到了用积分检验来刻划其加权部分和的极限定理,作为推论还得到了Chover型重对数律.把这些结果应用到经典的可和方式,获得了相应的结果. 这些结果推广了已知的一些结论.

关键词: NA随机变量, 重尾分布, 重对数律, 积分检验, 加权部分和

Abstract:

We establish the integral test for the weighted partial sums of identically distributed NA random variables with heavy-tailed distribution assumption by using the exponential inequality, and obtain the Chover's law of iterated logarithm as a corollary. As applications, the corresponding limit results for some classical summable methods are also established. These results in this paper extend the related known works in the literature.

Key words: NA random variables, Heavy-tailed distribution, Law of iterated logarithm, Integral test, Weighted partial sums

中图分类号:

60F15

邱德华, 陈平炎. NA随机变量序列加权和的Chover型重对数律[J]. 数学物理学报, 2014, 34(3): 674-683.

QIU De-Hua, CHEN Ping-Yan. Chover´s Law of Iterated Logarithm for Weighted Partial Sums of NA Random Variables Sequences[J]. Acta mathematica scientia,Series A, 2014, 34(3): 674-683.

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