一类随机变量序列关于Γ-分布的强偏差定理  

Strong deviation theorems for a class of random variable sequence on Γ-distribution

作　　者：杨卫国[1] 王康康[1] 

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2005年第4期320-323,共4页Journal of Jiangsu University：Natural Science Edition

基　　金：江苏省教育厅自然科学基金资助项目(02KJD110003)

摘　　要：引进似然比作为非负连续型随机变量序列相对于服从Γ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,在此子集上运用鞅方法得到了任意非负连续型随机变量序列的一类用不等式表示的强极限定理,将任意随机变量序列关于乘积分布的强偏差定理从离散状态空间推广到连续状态空间.作为推论得到了任意非负连续型随机变量序列关于指数分布,厄兰分布以及χ2-分布的强偏差定理以及服从Γ-分布的独立随机变量序列的一族强大数定律.The notion of the likelihood ratio, as a measure of deviation between a sequence of nonnegative continuous random variables and a sequence of independent random variables with Γ-distribution,is introduced. A subset of the sample space is given by restricting the likelihood ratio. On this subset a class of limit theorems, represented by inequalities, for the sequence of arbitrary nonnegative continuous random variables are obtained. The strong deviation theorem is generalized from the discrete space to the continuous space. And as corollaries of the strong deviation theorems of random variables on Γ-distribution, a class of the strong laws of sequences of exponential and χ~2-distribution random variables, are obtained.

关 键 词：概率论 强偏差定理 上鞅 强大数定理 随机变量序列 

分 类 号：O211.6[理学—概率论与数理统计]