A class of strong deviation theorems for the sequence of real valued random variables with respect to continuous-state non-homogeneous Markov chains

Abstract

In this paper, we consider the asymptotic behavior of the log-likelihood ratio as a measure of the deviation between a sequence of real valued random variables and a continuous-state non-homogeneous Markov chains. Then, by using the supermartingale limit theorem, we establish a class of strong deviation theorems for bivariate functions of the sequence of real valued random variables which are associated with the continuous-state non-homogeneous Markov chains.