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doi:10.3969/j.issn.1001-4268.2017.04.006

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Abstract

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.

Key words�� two rooted tree nonhomogeneous bifurcating Markov chains strong law of large numbers Shannon-McMillan theorem

PACS:	O211.4
	O211.6

About author:: ZHANG Yan; YANG WeiGuo

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Cite this article:

ZHANG Yan,YANG WeiGuo. The Strong Law of Large Numbers and the#br# Shannon-McMillan Theorem for Nonhomogeneous#br# Bifurcating Markov Chains Indexed by a Binary Tree[J]. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2017, 33(4): 408-416.

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http://aps.ecnu.edu.cn/EN/10.3969/j.issn.1001-4268.2017.04.006 OR http://aps.ecnu.edu.cn/EN/Y2017/V33/I4/408

[1]	YUAN Dailin, ZHAO Lianwen, LIU Cheng. Strong Law of Large Numbers of Sequences of Dependent Gaussian and Nonnegative Random Variables[J]. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2016, 32(3): 261-269.