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

Author

Hui Dang ; Weiguo Yang ; Zhiyan Shi

Author_Institution

Dept. of Math., Shanghai Jiao Tong Univ., Shanghai, China

Volume

61

Issue

4

fYear

2015

fDate

Apr-15

Firstpage

1640

Lastpage

1648

Abstract

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.

Keywords

Markov processes; trees (mathematics); binary tree; cellular aging detection; entropy ergodic theorem; finite state space; general state space; nonhomogeneous bifurcating Markov chains; Aging; Binary trees; Convergence; Educational institutions; Entropy; Markov processes; Random variables; Binary tree; binary tree; entropy ergodic theorem; nonhomogeneous bifurcating Markov chains; strong law of large numbers;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2015.2404310

Filename

7042766