摘要
引入极限相对对数似然比的概念,作为离散相依随机变量序列与独立随机变量序列的偏差的一种度量,并利用它来研究离散相依随机变量序列的极限性质.引入一种全新的概率研究方法——分析法,得到了一类用不等式表示的强极限定理,即强偏差定理,其偏差界依赖于此极限相对对数似然比.作为推论得到了经典的独立随机变量序列的强大数定理,进一步发展和完善了状态空间离散有限的随机变量序列关于乘积分布的强偏差定理.
The notion of limit relative log-likelihood ratio is introduced to investigate the limit properties of the sequence of dependent discrete random variables. A class of strong limit theorems represented by inequalities which we call the strong deviation theorems are obtained. The bounds given by these theorems depend on it. And as corollaries, the strong laws of sequences of independent variables are obtained.
出处
《江苏大学学报(自然科学版)》
EI
CAS
北大核心
2007年第2期176-179,共4页
Journal of Jiangsu University:Natural Science Edition
基金
国家自然科学基金资助项目(10571076)
关键词
离散相依随机变量序列
强偏差定理
极限相对对数似然比
sequence of dependent discrete variables
strong deviation theorems
limit relative log-likelihood.