Asymptotic equipartition property for second-order circular Markov chains indexed by a two-rooted Cayley tree. Issue 3 (1st February 2017) - Huang, Huilin; Yang, Weiguo; Shi, Zhiyan
ABSTRACT: In this paper, we introduce a model of a second-order circular Markov chain indexed by a two-rooted Cayley tree and establish two strong law of large numbers and the asymptotic equipartition property (AEP) for circular second-order finite Markov chains indexed by this homogeneous tree. In the proof, we apply a limit property for a sequence of multi-variable functions of a non homogeneous Markov chain indexed by such tree. As a corollary, we obtain the strong law of large numbers and AEP about the second-order finite homogeneous Markov chain indexed by the two-rooted homogeneous tree.