| 关于有限马氏链相对熵密度和随机条件熵的一类极限定理 |
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| 引用本文： | 刘文,杨卫国.关于有限马氏链相对熵密度和随机条件熵的一类极限定理[J].应用数学学报,1995,18(2):234-247. |
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| 作者姓名： | 刘文 杨卫国 |
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| 作者单位： | 河北工学院数学系，河北煤炭建工学院基础部 |
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| 摘 要： | 本文引进有限非齐次马链随机条件熵的概念，研究这个概念与相对熵密度的关系，并通过数列的绝对平均收敛的概念给出了有限非齐次马氏链的相对频率，相对熵密度和平均随机条件熵ａ．ｅ收敛于常数及有限非齐次马氏链熵率存在的条件。
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| 关 键 词： | 马氏链 相对熵密度 随机条件熵 极限定理 |
A CLASS OF LIMIT THEOREMS FOR THE RELATIVE ENTROPY DENSITY AND THE RANDOM CONDITIONAL ENTROPY OF FINITE MARKOV CHAINS |
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| LIU,WEN.A CLASS OF LIMIT THEOREMS FOR THE RELATIVE ENTROPY DENSITY AND THE RANDOM CONDITIONAL ENTROPY OF FINITE MARKOV CHAINS[J].Acta Mathematicae Applicatae Sinica,1995,18(2):234-247. |
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| Authors: | LIU WEN |
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| Abstract: | In this paper, the notion of random conditional entropy of finite nonhomogeneous markov chains is introduced, and the relation between this notion and the relative entropy density is studied. The condition of existence of the entropy rate of nonhomogeneous markov chains {X_n} and the conditions in which the relative frequency, the relative entropy density and the average random conditional entropy density and the average random conditional entropy of {X_n) are a.e. convergence to a constant are given by using the notion of absolute convergence in mean of the sequence. |
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| Keywords: | Nonhomogeneous Markov chains relative entropy density random conditional entropy a e convergence |
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