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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
Shi Zhiyan, Han Dazhao, Yang Weiguo
Faculty of Science, Jiangsu University
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.