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

令{X,Xn,n≥1}为同分布的NA随机变量序列,{an,n≥1}是一正常数序列且an/n↑.讨论了{X,Xn,n≥1}的强大数定律和完全收敛性,得到了与条件∞∑n=1P(|X|>an)<∞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.

Let {X, Xn, n≥ 1 } be a sequence of negatively associated random variables with identical distribution, {an ,n≥1} be a sequence of positive constants with a,/n ~. The strong law of large numbers and complete convergence for {X,Xn,n≥1} were obtained. These results are equivalent to the generalmoment condition∞∑n=1P（｜X｜〉an）〈∞ .On the other hand, the results extend the corresponding ones forpairwise independent random variables with identical distribution.