A class of strong deviation theorems for the random fields associated with bifurcating Markov chains indexed by a binary tree. Issue 5 (4th March 2021)

• Record Type: Journal Article
• Authors: Zhong, Pingping; Shi, Zhiyan; Yang, Weiguo; Min, Fan
• Is Part Of: Communications in statistics. Volume 50:Issue 5(2021)
• Page Start: 1210
• Page End: 1227
• Publication Date: 2021-03-04
• Subjects: Binary tree -- bifurcating Markov chain -- strong deviation theorem -- asymptotic equipartition property -- strong law of large numbers; 60F15 -- 60J10; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1648830
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this paper, we first introduce the asymptotic logarithmic likelihood ratio as a measure of the deviation between the arbitrary random fields and the bifurcating Markov chain on a binary tree. Then a class of strong deviation theorems for the random fields associated with bifurcating Markov chains indexed by a binary tree is established by constructing a nonnegative martingale. As corollaries, we obtain the strong law of large numbers (SLLN) and the asymptotic equipartition property (AEP) for the bifurcating Markov chains indexed by a binary tree.