广义赌博系统中任意随机变量序列关于Poisson分布的一类强偏差定理

摘要

In this paper, the notion of the limit logarithm likelihood ratio, as a measure of deviation between a sequence of the integer-valued random variables and a sequence of independent random variables with the Pois-son distribution , is introduced. A subset of the sample space is given by restricting the likelihood ratio, and on this subset a class of strong limit theorems for the sequence of arbitrary integer-valued random variables on the generalized gambling system are obtained. As corollaries, a class of the strong laws for sequences of independent random variables with Poisson distributions are obtained.%本文引进极限对数似然比作为任意随机变量序列相对于服从Poisson分布的独立随机变量序列的偏差的一种度量,并通过限制似然比给出了样本空间的一个子集,在此子集上得到了赌博系统中任意随机变量序列的一类用不等式表示的强极限定理.作为推论,得到了广义赌博系统服从Poisson分布的独立随机变量序列的一族强大数定理.