A class of strong deviation theorems for the sequence of nonnegative integer valued random variables

We consider the logarithm of the likelihood ratio between the sequence of the nonnegative integer valued random variables and the independent product distribution, establishing strong deviation theorems on the subset. As a corollary, we obtain classical strong laws of large numbers of Kolmogorov type for dependent random sequences with different distributions. Moreover, we discuss the deviation estimation for nonhomogeneous Markov chains.