On the strong laws of large numbers for weighted sums of random variables

被引：2
|
作者：
Chen, Pingyan [1 ]
Sung, Soo Hak [2 ]
机构：
[1] Jinan Univ, Dept Math, Guangzhou 510630, Guangdong, Peoples R China
[2] Pai Chai Univ, Dept Appl Math, Daejeon 35345, South Korea
来源：
STATISTICS & PROBABILITY LETTERS | 2016年 / 118卷
基金：
新加坡国家研究基金会; 中国国家自然科学基金;
关键词：
Strong law of large numbers; Weighted sums; Almost sure convergence; JOINT DISTRIBUTIONS;
D O I：
10.1016/j.spl.2016.06.020
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Let {X-n, n >= 1} be a sequence of random variables which is stochastically dominated by a random variable. Let {a(n), n >= 1} and {b(n), n >= 1} be sequences of real numbers with 0 < b(n) up arrow infinity. Sufficient conditions are given under which Sigma(n)(i=1) a(i)X(i),/b(n) -> 0 almost surely. No conditions are imposed on the joint distributions of the {X-n}. Our results generalize and improve some known results of the strong law of large numbers for random variables. We also give two examples which show the sharpness of our results. (C) 2016 Elsevier B.V. All rights reserved.
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页码：87 / 93
页数：7
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