| 杨洁,杨卫国.关于树指标非齐次马氏链的广义熵遍历定理[J].数学年刊A辑,2020,41(1):099~114 |
| 关于树指标非齐次马氏链的广义熵遍历定理 |
| The Generalized Entropy Ergodic Theorem for Nonhomogeneous Markov Chains Indexed by a Cayley Tree |
| Received:December 08, 2016 Revised:November 18, 2018 |
| DOI：10.16205/j.cnki.cama.2020.0008 |
| 中文关键词: Cayley tree, Nonhomogeneous Markov chains indexed bytrees, Strong law of large numbers, Generalized entropy ergodictheorem |
| 英文关键词:Cayley tree, Nonhomogeneous Markov chains indexed bytrees, Strong law of large numbers, Generalized entropy ergodictheorem |
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| 中文摘要: |
| 主要研究了树指标非齐次马氏链的广义熵遍历定理.
首先证明了树指标非齐次马氏链上的二元函数延迟平均的强极限定理.
然后得到了树指标非齐次马氏链上状态出现延迟频率的强大数定律,
以及树指标非齐次马氏链的广义熵遍历定理. 作为推论, 推广了一些已有结果.
同时, 证明了局部有限无穷树树指标有限状态随机过程广义熵密度的一致可积性. |
| 英文摘要: |
| In this paper, the authors study the generalized
entropy ergodic theorem for nonhomogeneous Markov chains indexed by
a Cayley tree. Firstly, they prove a strong limit theorem for the
delayed sums of the bivariate functions of nonhomogeneous Markov
chains indexed by a tree. Secondly, the strong law of large numbers
of the frequencies of occurrence of states of delayed sums and the
generalized entropy ergodic theorem for nonhomogeneous Markov chains
indexed by a Cayley tree are obtained. As corollaries, they
generalize some known results. The authors also prove that the
generalized entropy densities for arbitrary finite tree-indexed
stochastic processes are uniformly integrable. |
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