相依随机变量列的极限定理

Limit Theorems for the Sequence of Associated Random Variables

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.