Likelihood ratio and a class of strong laws for the sequence of integer-valued random variables

In this paper, the notion of likelihood ratio, as a measure of the deviation between a sequence of integer-valued random variables and an independent random sequence with Poisson distribution is introduced, and a class of strong laws, expressed by inequalities, on certain sets determined by this notion, are obtained. A class of strong laws for a sequence of independent Poisson random variables are special cases of the results of this paper.