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

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  • Zhiyan Shi
  • Weiguo Yang
  • Bei Wang

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.

Suggested Citation

  • Zhiyan Shi & Weiguo Yang & Bei Wang, 2016. "A class of small deviation theorems for the random variables associated with mth-order asymptotic circular Markov chains," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(23), pages 7027-7039, December.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:23:p:7027-7039
    DOI: 10.1080/03610926.2014.972746
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