矩条件下NA随机变量的强极限定理

doi:10.3969/j.issn.0253-2778.2015.06.005

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (6): 460-464.DOI: 10.3969/j.issn.0253-2778.2015.06.005

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矩条件下NA随机变量的强极限定理

夏凤熙，邓新，郑璐璐，王学军

安徽大学数学科学学院，安徽合肥 230601

收稿日期:2014-06-04 修回日期:2014-09-22 接受日期:2014-09-22 出版日期:2014-09-22 发布日期:2014-09-22
通讯作者: 王学军
作者简介:夏凤熙，女，1989年生，硕士. 研究方向：概率极限理论. E-mail: 1046549063@qq.com
基金资助:
国家自然科学基金项目(11201001)，安徽省自然科学基金项目(1508085J06)，安徽大学研究性教学示范课程（xjyjkc1407)，安徽大学研究生创新项目资助.

Strong limit theorems for negatively associated random variables with general moment conditions

XIA Fengxi, DENG Xin, ZHENG Lulu, WANG Xuejun

School of Mathematical Sciences, Anhui University, Hefei 230601, China

Received:2014-06-04 Revised:2014-09-22 Accepted:2014-09-22 Online:2014-09-22 Published:2014-09-22

摘要/Abstract

摘要： 令{X,Xn,n≥1} 为同分布的NA随机变量序列,{an,n≥1} 是一正常数序列且an/n↑.讨论了{X,Xn,n≥1}的强大数定律和完全收敛性,得到了与条件∑∞[]n=1P(|X|>an)<∞等价的结果. 另外,该结果推广了关于两两独立同分布序列的相应结果.

关键词: 强大数定律, NA随机变量, 完全收敛性

Abstract: Let {X,Xn,n≥1} be a sequence of negatively associated random variables with identical distribution, {an,n≥1} be a sequence of positive constants with an/n↑. The strong law of large numbers and complete convergence for {X,Xn,n≥1} were obtained. These results are equivalent to the general moment condition ∑∞[]n=1P(|X|>an)<∞. On the other hand, the results extend the corresponding ones for pairwise independent random variables with identical distribution.

Key words: strong law of large numbers, negatively associated random variables, complete convergence

中图分类号:

O211.

夏凤熙，邓新，郑璐璐，王学军. 矩条件下NA随机变量的强极限定理[J]. 中国科学技术大学学报, 2015, 45(6): 460-464.

XIA Fengxi, DENG Xin, ZHENG Lulu, WANG Xuejun. Strong limit theorems for negatively associated random variables with general moment conditions[J]. Journal of University of Science and Technology of China, 2015, 45(6): 460-464.

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矩条件下NA随机变量的强极限定理

Strong limit theorems for negatively associated random variables with general moment conditions

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