相依随机变量列的极限定理  

Limit Theorems for the Sequence of Associated Random Variables

作　　者：郭进利[1] 

机构地区：[1]上海理工大学管理学院,上海200093

出　　处：《工程数学学报》2007年第3期469-474,共6页Chinese Journal of Engineering Mathematics

基　　金：上海市重点学科建设项目(T0502);上海市教委自然科学基金(05EZ35).

摘　　要：相依随机变量列是否有大数定律是可靠性理论和管理科学中经常遇到的问题。本文讨论了相依随机变量列的极限定理,获得了渐近负相关随机变量列的大数律,且伯恩斯坦大数律可作为本文结果的特例。特别是,获得了Loéve定理的一个等价形式,并讨论了相依随机变量列部分和上升的阶。Studied in this paper is the limit for associated random sequences in engineering statistics. We introduce an ANA （asymptotical negatively associated） random sequence and obtain some laws of large numbers for asymptotical negatively associated random sequences. The well-known Bernstein law of large numbers can be deduced from our results. An equivalent theorem for the Loire theorem is obtained and the limit theorem for estimation of sum of associated random sequences is also studied.

关 键 词：两两NQD列 随机变量列 大数律 Loéve定理 

分 类 号：O211.4[理学—概率论与数理统计]