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)

• Record Type: Journal Article
• Authors: Shi, Zhiyan; Ji, Jinli; Yang, Weiguo
• Is Part Of: Communications in statistics. Volume 46:Issue 14(2017)
• Page Start: 6823
• Page End: 6830
• Publication Date: 2017-07-18
• Subjects: Markov chains -- Shannnon–McMillan theorem -- small deviation theorems; 60J10 -- 60F15; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1137594
• Languages: English
• ISSNs: 0361-0926

Abstract

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.