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) - Zhong, Pingping; Shi, Zhiyan; Yang, Weiguo; Min, Fan
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.