张艳, 杨卫国. 二叉树分枝马氏链的强大数定律和Shannon-McMillan定理[J]. 应用概率统计, 2017, 33(4): 408-416. DOI: 10.3969/j.issn.1001-4268.2017.04.006
引用本文: 张艳, 杨卫国. 二叉树分枝马氏链的强大数定律和Shannon-McMillan定理[J]. 应用概率统计, 2017, 33(4): 408-416. DOI: 10.3969/j.issn.1001-4268.2017.04.006
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ZHANG Yan, YANG WeiGuo. The Strong Law of Large Numbers and the Shannon-McMillan Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree[J]. Chinese Journal of Applied Probability and Statistics, 2017, 33(4): 408-416. DOI: 10.3969/j.issn.1001-4268.2017.04.006
Citation: ZHANG Yan, YANG WeiGuo. The Strong Law of Large Numbers and the Shannon-McMillan Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree[J]. Chinese Journal of Applied Probability and Statistics, 2017, 33(4): 408-416. DOI: 10.3969/j.issn.1001-4268.2017.04.006
shu

二叉树分枝马氏链的强大数定律和Shannon-McMillan定理

The Strong Law of Large Numbers and the Shannon-McMillan Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree

    摘要
  • 摘要: 首先研究二叉树有限状态分枝马氏链的随机序偶出现频率的强大数定律, 之后研究二叉树有限状态分枝马氏链函数的强大数定律, 作为推论得到二叉树有限状态分枝马氏链的Shannon-McMillan定理.

     

    Abstract: In this paper, we first study the strong law of large numbers for the frequencies of occurrence of random ordered couples of states for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Then the strong law of large numbers are studied for functions of the nonhomogeneous bifurcating Markov chains indexed by a binary tree. As a corollary, we obtain the shannon-McMillan theorem for these Markov chains with finite state space.

     

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