| 任意齐次树指标马氏链场的一类Shannon-Mcmillan定理 |
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| 引用本文： | 方次军,王康康.任意齐次树指标马氏链场的一类Shannon-Mcmillan定理[J].数学的实践与认识,2014(22). |
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| 作者姓名： | 方次军 王康康 |
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| 作者单位： | 湖北工业大学理学院;江苏科技大学数理学院; |
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| 基金项目： | 江苏省高校自然科学基金(09KJD110002) |
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| 摘 要： | 采用构造相容分布与非负上鞅的方法来研究任意齐次树指标可列非齐次马氏链场的相对熵密度的一类强极限定理,并由此得出若干齐次树指标有限状态非齐次马氏链场、一般非齐次马氏链的Shannon-Mcmillan定理.将已有的关于离散信源的结果加以推广.
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| 关 键 词： | Shannon-Mcmillan定理 齐次树 非齐次 马氏链场 相容分布 相对熵密度 |
A Class of Shannon-Mcmillan Theorems for Markov Chains Field Indexed by a Homogeneous Tree |
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| Abstract: | In this paper,a class of strong limit theorems for the relative entropy densities of Markov chains fleld indexed by a homogeneous tree are discussed by constructing the joint distribution and nonnegative super martingales.As corollaries,some Shannon-Mcmillan theorems for the finite Markov chains field indexed by a homogeneous tree,the general nonhomogeneous Markov chain are obtained and some results for the discrete information source which have been obtained by author are extended. |
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| Keywords: | Shannon-Mcmillan theorem homogeneous tree Markov chains field consistent distribution relative entropy density |
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