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Strong Law of Large Numbers for Countable Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degree

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Listed:
  • Bao Wang
  • Weiguo Yang
  • Zhiyan Shi
  • Qingpei Zang

Abstract

We study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by an infinite tree with uniformly bounded degree, which extends the corresponding results of countable Markov chains indexed by a Cayley tree and generalizes the relative results of finite Markov chains indexed by a uniformly bounded tree.

Suggested Citation

  • Bao Wang & Weiguo Yang & Zhiyan Shi & Qingpei Zang, 2014. "Strong Law of Large Numbers for Countable Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degree," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:325361
    DOI: 10.1155/2014/325361
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    References listed on IDEAS

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    1. 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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