The strong law of large numbers and the Shannon-McMillan theorem for the mth-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree

摘要

In this article, we studied the strong law of large numbers(LLN) and Shannon-McMillan theorem for an mth-order nonhomogeneous Markov chain indexed by an m- rooted Cayley tree. This article generalized the relative results of level mth-order nonhomogeneous Markov chains indexed by an m- rooted Cayley tree.