Table of Contents
ISRN Probability and Statistics
Volume 2012, Article ID 768657, 11 pages
http://dx.doi.org/10.5402/2012/768657
Research Article

Strong Law of Large Numbers for Hidden Markov Chains Indexed by Cayley Trees

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

Received 13 July 2012; Accepted 31 July 2012

Academic Editors: N. Chernov, F. Fagnola, P. Neal, and H. J. Paarsch

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 extend the idea of hidden Markov chains on lines to the situation of hidden Markov chains indexed by Cayley trees. Then, we study the strong law of large numbers for hidden Markov chains indexed by Cayley trees. As a corollary, we get the strong limit law of the conditional sample entropy rate.