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A class of small deviation theorem for the sequences of countable state random variables with respect to homogeneous Markov chains

Author

Listed:
  • Zhiyan Shi
  • Jinli Ji
  • Weiguo Yang

Abstract

Let {Xn, n ⩾ 0} be a sequence of random variables on the probability space (Ω,F,P)$(\Omega ,{\cal F},P)$ taking values in alphabet S = {0, 1, 2, …}. Let Q be another probability measure on F${\cal F}$, under which {Xn, n ⩾ 0} is a homogeneous Markov chain. Let h(P∣Q) be the sample divergence rate of P with respect to Q related to {Xn, n ⩾ 0}. In this paper, the authors obtain several strong laws of large numbers and Shannnon–McMillan theorem for countable state homogeneous Markov chains by establishing the small deviation theorems of {Xn, n ⩾ 0} with respect to countable state homogeneous Markov chain.

Suggested Citation

  • Zhiyan Shi & Jinli Ji & Weiguo Yang, 2017. "A class of small deviation theorem for the sequences of countable state random variables with respect to homogeneous Markov chains," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 6823-6830, July.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:14:p:6823-6830
    DOI: 10.1080/03610926.2015.1137594
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