Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 536530, 9 pages
http://dx.doi.org/10.5402/2012/536530
Research Article

Strong Law of Large Numbers of the Offspring Empirical Measure for Markov Chains Indexed by Homogeneous Tree

College of Mathematics and Information Science, Wenzhou University, Zhejiang 325035, China

Received 24 December 2011; Accepted 26 January 2012

Academic Editors: K. Karamanos and E. Yee

Copyright © 2012 Huilin Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the limit law of the offspring empirical measure and for Markov chains indexed by homogeneous tree with almost everywhere convergence. Then we prove a Shannon-McMillan theorem with the convergence almost everywhere.