The Strong Law of Large Numbers and the Shannon-McMillan Theorem for the Two-Order Nonhomogeneous Markov Chains Indexed by an Two Rooted Cayley Tree

In this paper, we first study the strong convergence theorem for finite two-order nonhomogeneous Markov chains indexed by an two rooted Cayley tree, then we obtain the strong law of large numbers for this Markov chains. Finally, we obtain the Shannon-McMillan theorem with a.e. convergence for an two-order nonhomogeneous Markov chain indexed by an two rooted Cayley tree.