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The strong law of large numbers and the Shannon–McMillan theorem for nonhomogeneous Markov chains indexed by a Cayley tree

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  • Dong, Yan
  • Yang, Weiguo
  • Bai, Jianfang

Abstract

In this paper, we study the strong law of large numbers and the Shannon–McMillan theorem for nonhomogeneous Markov chains indexed by a Cayley tree. This article generalizes the relative results of level nonhomogeneous Markov chains indexed by a Cayley tree.

Suggested Citation

  • Dong, Yan & Yang, Weiguo & Bai, Jianfang, 2011. "The strong law of large numbers and the Shannon–McMillan theorem for nonhomogeneous Markov chains indexed by a Cayley tree," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1883-1890.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1883-1890
    DOI: 10.1016/j.spl.2011.06.021
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    References listed on IDEAS

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    1. Liu, Wen & Yang, Weiguo, 2000. "The Markov approximation of the sequences of N-valued random variables and a class of small deviation theorems," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 117-130, September.
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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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