共查询到19条相似文献,搜索用时 265 毫秒
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该文引进广义Bethe树和广义Cayley树的概念,并研究其上马氏链场关于状态和状态序偶出现频率的强极限定理,作为主要结果的推论,得到Bethe树和Cayley树上马氏链场的ShannonMcMillan定理.证明中采用了研究概率论强极限定理的一种新的方法. 相似文献
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研究给出了非齐次树上m重非齐次马氏链的一类强偏差定理. 相似文献
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马丽娜 《纯粹数学与应用数学》2007,23(4):549-555
通过构造两个非负鞅证明了一个强极限定理,然后把它应用到本文所定义的广义Bethe树上的奇偶马尔可夫链场上,从而获得了此马氏链场上的一类强极限定理. 相似文献
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刘宝慧 《数学的实践与认识》2016,(21):262-267
在二叉树上分支马氏链的等价性质研究的基础上,给出了三叉树上分支马氏链定义的离散形式,除了把二叉树上分支马氏链的两个等价性质平移到三叉树上分支马氏链以外,又给出了三叉树上分支马氏链的两个等价性质及两个性质.得出结论的关键方法是在概率乘积公式及条件概率公式的计算中正确处理其中所涉及到的许多繁杂的必然事件. 相似文献
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树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强偏差定理一直是国际概率论界研究的中心课题之一.通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,研究给出了一类非齐次树上连续状态马氏链滑动平均的若干强偏差定理. 相似文献
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In this paper, we first study the strong law of large
numbers for the frequencies of occurrence of random ordered couples of states
for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Then
the strong law of large numbers are studied for functions of the nonhomogeneous
bifurcating Markov chains indexed by a binary tree. As a corollary, we obtain
the shannon-McMillan theorem for these Markov chains with finite state space. 相似文献
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Shi Zhiyan Wang Zhongzhi Zhong Pingping Fan Yan 《Journal of Theoretical Probability》2022,35(3):1367-1390
Journal of Theoretical Probability - In this paper, we study the generalized entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Firstly, by constructing... 相似文献
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Weiguo Yang 《随机分析与应用》2013,31(2):220-237
In this article, we establish a class of strong deviation theorems for the random fields which are associated with nonhomogeneous Markov chains indexed by a Bethe tree. As corollaries, we obtain the strong law of large numbers and asymptotic equipartition property for nonhomogeneous Markov chains indexed by such tree. 相似文献
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利用一致有界树指标马氏链的强大数定律,给出了一致有界树指标马氏链的关于状态和状态序偶出现的层频率的强大数定律. 相似文献
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In this paper, we are going to study the strong laws of large numbers for asymptotic even–odd Markov chains indexed by a homogeneous tree. First, the definition of the asymptotic even–odd Markov chain is introduced. Then the strong limit theorem for asymptotic even–odd Markov chains indexed by a homogeneous tree is established. Next, the strong laws of large numbers for the frequencies of occurrence of states and ordered couple of states for asymptotic even–odd Markov chains indexed by a homogeneous tree are obtained. Finally, we prove the asymptotic equipartition property (AEP) for these Markov chains. 相似文献
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Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree 总被引:3,自引:0,他引:3
In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree. 相似文献
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树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强极限定理一直是国际概率论界研究的中心课题之一.研究给出了一类非齐次树上马氏链的一个强极限定理. 相似文献