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

Let {X n , n ⩾ 0} be a sequence of random variables on the probability space taking values in alphabet S = {0, 1, 2, ...}. Let Q be another probability measure on , under which {X n , n ⩾ 0} is a homogeneous Markov chain. Let h(P∣Q) be the sample divergence rate of P with respect to Q related to {X...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2017-07, Vol.46 (14), p.6823-6830
Main Authors: Shi, Zhiyan, Ji, Jinli, Yang, Weiguo
Format: Article
Language:English
Subjects:
Markov analysis
Markov chains
Random variables
Shannnon-McMillan theorem
small deviation theorems
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Summary:Let {X n , n ⩾ 0} be a sequence of random variables on the probability space taking values in alphabet S = {0, 1, 2, ...}. Let Q be another probability measure on , under which {X n , n ⩾ 0} is a homogeneous Markov chain. Let h(P∣Q) be the sample divergence rate of P with respect to Q related to {X n , 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 {X n , n ⩾ 0} with respect to countable state homogeneous Markov chain.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2015.1137594