Asymptotic equipartition property for second-order circular Markov chains indexed by a two-rooted Cayley tree. Issue 3 (1st February 2017)

• Record Type: Journal Article
• Authors: Huang, Huilin; Yang, Weiguo; Shi, Zhiyan
• Is Part Of: Communications in statistics. Volume 46:Issue 3(2017)
• Page Start: 1275
• Page End: 1289
• Publication Date: 2017-02-01
• Subjects: Asymptotic equipartition property -- second-order circular Markov chain -- strong law of large numbers -- two-rooted Cayley tree.; 60C05 -- 05C80; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1014113
• Languages: English
• ISSNs: 0361-0926

Abstract

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.