Asymptotic equipartition property for second-order circular Markov chains indexed by a two-rooted Cayley tree

Huilin Huang, Weiguo Yang and Zhiyan Shi

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 3, 1275-1289

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.

Date: 2017
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DOI: 10.1080/03610926.2015.1014113

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