The generalized entropy ergodic theorem for Markov chains indexed by a spherically symmetric tree

Abstract

In information theory, the entropy ergodic theorem is a fundamental one well-known to all. In this article, we will study the generalized entropy ergodic theorem for Markov chains indexed by a spherically symmetric tree. First, we give the definition of Markov chains indexed by a spherically symmetric tree. Meanwhile, the generalized strong law of large numbers for Markov chains indexed by a spherically symmetric tree is proved. Finally, we obtain the generalized entropy ergodic theorem for Markov chains indexed by a spherically symmetric tree.