A class of small deviation theorems for the random variables associated with mth-order asymptotic circular Markov chains

Zhiyan Shi, Weiguo Yang and Bei Wang

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 23, 7027-7039

Abstract: In this article, we study a class of small deviation theorems for the random variables associated with mth-order asymptotic circular Markov chains. First, the definition of mth-order asymptotic circular Markov chain is introduced, then by applying the known results of the limit theorem for mth-order non homogeneous Markov chain, the small deviation theorem on the frequencies of occurrence of states for mth-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 mth-order nonhomogeneous Markov chains are given.

Date: 2016
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DOI: 10.1080/03610926.2014.972746

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