CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2015, 31(2) 125-134 DOI:      ISSN: 1001-4268 CN: 31-1256

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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

Abstract��

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.

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