A class of small deviation theorems for the random variables associated with mth-order asymptotic circular Markov chains. Issue 23 (1st December 2016) - Shi, Zhiyan; Yang, Weiguo; Wang, Bei
ABSTRACT: In this article, we study a class of small deviation theorems for the random variables associated with m th-order asymptotic circular Markov chains. First, the definition of m th-order asymptotic circular Markov chain is introduced, then by applying the known results of the limit theorem for m th-order non homogeneous Markov chain, the small deviation theorem on the frequencies of occurrence of states for m th-order asymptotic circular Markov chains is established. Next, the strong law of large numbers and asymptotic equipartition property for this Markov chains are obtained. Finally, some results of m th-order nonhomogeneous Markov chains are given.