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有限非齐次马尔可夫链的强极限定理 被引量:1

The strong limit theorems for finite nonhomogeneous Markov chains
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摘要 利用分析法研究了马氏链相对熵密度的若干极限性质,推广了Shannon—McMillan的极限定理,改进并推广了文[1]~[3]的主要结果,建立了新的有限非齐次马尔可夫链的强极限定理. The many properties of the relative entropy density were studied by using analysis method. The theorems of Shannon-McMillan were extended. Main results of article [ 1 ] - [ 3 ] were improved. The strong limit theorems of finite nonhomogeneous Markov chain were set up.
作者 王学武
出处 《南阳师范学院学报》 CAS 2007年第3期14-17,共4页 Journal of Nanyang Normal University
关键词 强极限定理 马尔可夫链 相对熵密度 strong limit theorem Markov chain entropy relative entropy density
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参考文献5

  • 1Liu Wen. Some strong limit theorems relative to the geometric average of random transition probabilities of arbitrary finite nonhomogeneous Markov chains[ J]. Stat. Probab. Letts, 1994,21 ( 1 ) :77 - 83.
  • 2Liu Wen and Yang Weiguo. An extention of Shannon-McMillan theorem and some limit properties for nonhomogenous Markov chains [ J ]. Stochastic Proc. Appl, 1996,61 ( 1 ) : 129 - 145.
  • 3Liu Wen and Wang Zhongzhi. A strong limit theorem on random selection for countable nonhomogenous Markov chains[ J].Chinese J. Math ( Taiwan), 1996,24 ( 2 ) : 187 - 197.
  • 4Liu Wen. A limit property of arbitrary discrete information sources[ J ]. Taiwan Residents J. Math, 1999,3 (4) :539 -546.
  • 5Kai lai chung. A course in probability theory[ M ]. New York: Academic press,1968:354- 360.

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