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.