Some strong limit theorems for nonhomogeneous Markov chains indexed by controlled trees

被引：0
作者：
Weicai Peng
Jie Liu
Yongchao Hou
Peishu Chen
Jueping Bu
机构：
[1] Shanghai University of Finance and Economics,School of International Business Administration
[2] Chaohu University,Department of Mathematics
[3] Huaibei Normal University,College of Mathematics and Science
来源：
Journal of Inequalities and Applications | / 2016卷
关键词：
nonhomogeneous Markov chain; controlled tree; strong law of large numbers; AEP;
D O I：
暂无
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学科分类号：
摘要：
In this paper, a kind of infinite, local finite tree T, named a controlled tree, is introduced. Some strong limit properties, such as the strong law of large numbers and the asymptotic equipartition property, for nonhomogeneous Markov chains indexed by T, are established. The outcomes are the generalizations of some well-known results.
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[1]  
Benjamini I(1994)Markov chains indexed by trees Ann. Probab. 22 219-243
[2]  
Peres Y(1990)Entropic aspects of random fields on trees IEEE Trans. Inf. Theory 36 1006-1018
[3]  
Berger T(1992)Antomorphism invariant measure on trees Ann. Probab. 20 1549-1566
[4]  
Ye Z(2001)Strong law of large numbers for branching Markov chains Markov Process. Relat. Fields 8 107-116
[5]  
Pemantle R(2013)A class of small deviation theorems for random fields on a uniformly bounded tree J. Inequal. Appl. 2013 3275-3280
[6]  
Takacs C(2007)The asymptotic equipartition property for nonhomogeneous Markov chains indexed by a homogeneous tree IEEE Trans. Inf. Theory 53 495-502
[7]  
Wang S(2001)Strong law of large numbers and Shannon-McMillan theorem for Markov chains field on Cayley tree Acta Math. Sci. Ser. B 21 241-250
[8]  
Yang WG(2003)Some limit properties for Markov chains indexed by a homogeneous tree Stat. Probab. Lett. 65 157-184
[9]  
Yang WG(1996)Ergodic, regular and asymptotic equipartition property of random fields on trees J. Comb. Inf. Syst. Sci. 21 411-422
[10]  
Ye Z(2004)Some strong limit theorems for Markov chain fields on trees Probab. Eng. Inf. Sci. 18 473-481
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