对数似然比与整值随机变量序列的一类强律

LOGARITHMIC LIKELIHOOD RATIO AND A CLASS OF STRONG LAWS FOR THE SEQUENCE OF INTEGER-VALUED RANDOM VARIABLES

本文引进对数似然比作为整值随机变量序列相对于服从几何分布的独立随机变量序列的偏差的一种度量,并通过限制对数似然比给出了样本空间的一个子集.在此子集上得到了一类用不等式表示的强律,其中包含整值随机变量序列与相对熵密度及几何分布的熵函数有关的若干极限性质.

In this paper, the notion of logarithmic likelihood ratio, as a measure of the deviation of a sequence of integer-valued random variables from an independent random sequence with geometric distribution, is introduced. By restricting the logarithmic likelihood ratio, a certain subset of the sample space is given, and on this subset, a class of strong laws, represented by inequalities, are obtained. These strong laws contain some limit properties of the sequence of integer-valued random variables, concerning relative entropy density and the entropy function of geometric distribution.