任意随机序列关于广义几何分布的一类强偏差定理  

Strong Deviation Theorems for the Sequence of Arbitrary Random Variables under the Generalized Geometric Distribution

作　　者：王康康[1] 杨卫国[2] 

机构地区：[1]江苏科技大学数理学院,镇江212003 [2]江苏大学理学院,镇江212013

出　　处：《工程数学学报》2008年第2期239-244,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10571076)．

摘　　要：本文引进对数似然比作为任意随机变量序列相对于服从广义几何分布的随机变量序列的偏差的一种度量,给出样本空间的一个子集。在该子集上通过构造非负上鞅和纯分析运算得到了任意随机变量序列关于广义几何分布的一类用不等式表示的强极限定理,即强偏差定理。作为推论得到了已有的随机变量序列关于几何分布的强偏差定理以及服从广义几何分布的任意随机变量序列的一类强大数定律。In this paper, the notion of the logarithmic likelihood ratio, as a measure of deviation between a sequence of arbitrary random variables and a sequence of independent random variables with the generalized geometric distribution, is introduced and a subset is given. On this subset a class of strong limit theorems, represented by inequalities, for the sequence of arbitrary random variables with respect to the generalized geometric distribution are obtained by constructing nonnegative superior martingale. The strong deviation theorem for the sequence of random variables with respect to geometric distribution and a class of the strong laws of large numbers for sequences of random variables with generalized geometric distribution are also obtained.

关 键 词：强偏差定理 广义几何分布 鞅 对数似然比 任意随机序列 

分 类 号：O211.6[理学—概率论与数理统计]