关于离散随机变量序列的一类强偏差定理

A class of strong deviation theorems for sequence of dependent discrete variables

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.