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任意信源关于赌博系统的一类Shannon-McMillan定理 被引量:5

A class of Shannon-Mcmillan theorems for arbitrary discrete information source on the gambling system
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摘要 采用网微分法和分析运算方法来研究赌博系统中任意随机变量序列随机条件熵的一类强极限定理,并由此得出若干任意信源的Shannon-Mcmillan定理.将已有的关于离散信源的结果加以推广. A class of strong limit theorems for the random conditional entropy densities of the sequence of arbitrary random variables on the gambling system are discussed by applying the differentiation on a net and analytical methods. As corollaries, some Shannon-Mcmillan theorems for arbitrary information source are obtained and some results for the discrete information source which has been obtained are extended.
作者 王康康
出处 《纯粹数学与应用数学》 CSCD 北大核心 2008年第2期353-357,共5页 Pure and Applied Mathematics
基金 江苏省高校自然科学基础研究项目(07KJD110048)
关键词 SHANNON-MCMILLAN定理 任意信源 随机条件熵 相对熵密度 Shannon-Mcmillan theorem, arbitrary information source, random conditional entropy, relative entropy density
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参考文献7

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  • 2Mcmillan B. The Basic Theorem of information theory[J]. Ann. Math. Statist., 1953, 24: 196-219.
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二级参考文献7

共引文献12

同被引文献35

  • 1金少华,宛艳萍,陈秀引,马中雪.非齐次树上m阶非齐次马氏链的一类强偏差定理[J].河北工业大学学报,2013,42(2):61-66. 被引量:2
  • 2汪忠志,杨卫国.二重非齐次马氏链及其随机变换的若干强极限定理[J].系统科学与数学,2004,24(4):451-462. 被引量:10
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  • 4Mcmillan B. The basic theorem of information theory[ J ]. Ann Math Statist, 1953 (24) : 196 - 219.
  • 5I Breiman L. The individual ergodic theorem of information theory[ J ]. Ann Math Statist, 1957 (28) : 809 - 811.
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  • 9Liu Wen, Yang Weiguo. An extension of Shannon-Mcmil- lan theorem and some limit properties for nonhomogeneous Markov chains [ J ]. Stochastic Process Appl, 1996 (61) : 129 - 145.
  • 10Doob J L. Stochastic process [ M ]. New York: Wiley, 1953:384.

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