A class of strong deviation theorems for the random fields associated with bifurcating Markov chains indexed by a binary tree

Pingping Zhong, Zhiyan Shi, Weiguo Yang and Fan Min

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 5, 1210-1227

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.

Date: 2021
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DOI: 10.1080/03610926.2019.1648830

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