The Strong Law of Large Numbers and the Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree

被引：23
|
作者：
Dang, Hui [1 ]
Yang, Weiguo [2 ]
Shi, Zhiyan [2 ]
机构：
[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
[2] Jiangsu Univ, Fac Sci, Zhenjiang 212013, Peoples R China
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2015年 / 61卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Binary tree; nonhomogeneous bifurcating Markov chains; strong law of large numbers; entropy ergodic theorem; SHANNON-MCMILLAN THEOREM; FIELDS;
D O I：
10.1109/TIT.2015.2404310
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Guyon (Guyon J. Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann Appl Probab, 2007, 17:1538-1569) introduced an important model for homogeneous bifurcating Markov chains indexed by a binary tree taking values in general state space and studied their limit theorems. The results were applied to detect cellular aging. In this paper, we define a discrete form of nonhomogeneous bifurcating Markov chains indexed by a binary tree and discuss the equivalent properties for them. The strong law of large numbers and the entropy ergodic theorem are studied for these Markov chains with finite state space. In contrast to previous work, we use a new approach to prove the main results of this paper.
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页码：1640 / 1648
页数：9
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