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

Zhiyan Shi, Jinli Ji and Weiguo Yang

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 14, 6823-6830

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.

Date: 2017
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DOI: 10.1080/03610926.2015.1137594

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