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Some limit properties for the mth-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree

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  • Shi, Zhiyan
  • Yang, Weiguo

Abstract

In this paper, we first study a convergence theorem for a finite mth-order nonhomogeneous Markov chain indexed by an m rooted Cayley tree. As corollaries, we obtain some limit theorems for the frequencies of occurrence of states for this Markov chain. Finally, we obtain the strong law of large numbers (LLN) and the Shannon-McMillan theorem for a class of finite mth-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree.

Suggested Citation

  • Shi, Zhiyan & Yang, Weiguo, 2010. "Some limit properties for the mth-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1223-1233, August.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:15-16:p:1223-1233
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    References listed on IDEAS

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    1. Yang, Weiguo & Liu, Wen, 2000. "Strong law of large numbers for Markov chains field on a Bethe tree," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 245-250, September.
    2. Yang, Weiguo, 2003. "Some limit properties for Markov chains indexed by a homogeneous tree," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 241-250, November.
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    Cited by:

    1. Zhiyan Shi & Zhongzhi Wang & Pingping Zhong & Yan Fan, 2022. "The Generalized Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1367-1390, September.

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