A class of small deviation theorem for the sequences of countable state random variables with respect to homogeneous Markov chains. Issue 14 (18th July 2017) - Shi, Zhiyan; Ji, Jinli; Yang, Weiguo
ABSTRACT: Let { Xn, 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 { 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.