| STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES |
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| 作者姓名： | 包振华 叶中行 |
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| 作者单位： | School of Mathematics Liaoning Normal University Dalian 116029，China，Department of Mathematics Shanghai Jiaotong University，Shanghai 200240，China |
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| 基金项目： | 国家重点基础研究发展计划(973计划)，国家自然科学基金 |
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| 摘 要： | Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.
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| 关 键 词： | Cayley树 非对称性马尔可夫链 渐进均分性 大数强制性 |
| 收稿时间： | 28 September 2005 |
| 修稿时间： | 2005-09-28 |
Strong law of large numbers and asymptotic equipartition property for nonsymmetric Markov chain fields on Cayley trees |
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| Bao Zhenhua,Ye Zhongxing,.STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES[J].Acta Mathematica Scientia,2007,27(4):829-837. |
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| Authors: | Bao Zhenhua Ye Zhongxing |
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| Institution: | School of Mathematics, Liaoning Normal University, Dalian 116029, China;Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China |
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| Abstract: | Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields (NSMC) on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields. The asymptotic equipartition properties with almost everywhere (a.e.) convergence for NSMC on Cayley trees are obtained. |
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| Keywords: | Cayley tree nonsymmetric Markov chain fields strong law of large numbers asymptotic equipartition property |
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