Table of Contents
International Journal of Stochastic Analysis
Volume 2014, Article ID 628321, 6 pages
http://dx.doi.org/10.1155/2014/628321
Research Article

Strong Law of Large Numbers for Hidden Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degrees

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

Received 29 August 2014; Accepted 24 November 2014; Published 9 December 2014

Academic Editor: Lukasz Stettner

Copyright © 2014 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 strong limit theorems for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees. We mainly establish the strong law of large numbers for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees and give the strong limit law of the conditional sample entropy rate.