随机选择系统中任意随机变量序列关于乘积分布的一类强偏差定理

Strong deviation theorems for the sequence of arbitrary random variables with respect to product distribution in random selection system

通过引进极限对数似然比的概念,作为任意随机变量序列相对于服从二项分布的独立随机变量序列的分布偏差的一种度量,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(又称随机选择系统)中任意随机变量序列的一类用不等式表示的强极限定理,作为推论得到了任意随机变量序列关于二项乘积分布的强偏差定理以及服从二项分布的独立随机变量序列的一族强大数定理.

As a measure of deviation between a sequence of the integer-valued random variables and a sequence of independent random variables with the biometric distribution,the notion of the limit logarithmic likelihood ratio was introduced in this paper.A subset of the sample space was given by restricting the likelihood ratio;and then,a class of limit theorems,which was represented by inequalities,was obtained based on this subset for the sequence of arbitrary integer-valued random variables on the gambling system.As corollaries,strong deviation theorems for arbitrary stochastic sequence on product biometric distribution were gotten.Moreover,a class of strong laws for sequences of independent random variables with biometric distributions was obtained.