LOGARITHMIC LIKELIHOOD RATIO AND A CLASS OF STRONG LAWS FOR THE SEQUENCE OF INTEGER-VALUED RANDOM VARIABLES
对数似然比与整值随机变量序列的一类强律

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.