Complete Moment Convergence for Sung's Type Weighted Sums of B-Valued Random Elements

被引：0

作者：

Li, Wei ^{[1
]}

Chen, Pingyan ^{[2
]}

Sung, Soo Hak ^{[3
]}

机构：

[1] Zhongkai Univ Agr & Engn, Coll Computat Sci, Guangzhou 510225, Guangdong, Peoples R China

[2] Jinan Univ, Dept Math, Guangzhou 510632, Guangdong, Peoples R China

[3] Pai Chai Univ, Dept Appl Math, Daejeon 302735, South Korea

来源：

DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2016年 / 2016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：

INDEPENDENT RANDOM ELEMENTS; STRONG LAW; RATES; REFINEMENT; ARRAYS; TAIL;

D O I：

10.1155/2016/1484160

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p >= 1/alpha and 1/2 < alpha <= 1. Let {X, X-n, n >= 1} be a sequence of independent and identically distributed B-valued random elements and let {a(ni), 1 <= i <= n, n >= 1} be an array of real numbers satisfying Sigma(n)(i=1) vertical bar a(ni)vertical bar(q) = O(n) for some q > p. We give necessary and sufficient conditions for complete moment convergence of the form Sigma(infinity)(i=1) n((p-v)alpha-2) E{parallel to Sigma(n)(i=1) a(ni)X(i)parallel to - epsilon n(alpha)}(+)(v) < infinity, for all epsilon > 0, where 0 < v < p. A strong law of large numbers for weighted sums of independent B-valued random elements is also obtained.

引用

页数：8

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