The Asymptotic Equipartition Property for Nonhomogeneous Markov Chains Indexed by a Homogeneous Tree

Abstract

In this correspondence, we first establish a strong limit theorem for countable nonhomogeneous Markov chains indexed by a homogeneous tree. As corollaries, we obtain some strong limit theorems for frequencies of occurrence of states and ordered couple of states for these Markov chains. Finally, we prove the strong law of large numbers and the asymptotic equipartition property (AEP) for finite nonhomogeneous Markov chains indexed by a homogeneous tree.