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Journal of Applied Mathematics
Volume 2014, Article ID 325361, 5 pages
http://dx.doi.org/10.1155/2014/325361
Research Article

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

1Faculty of Science, Jiangsu University, Zhenjiang 212013, China
2College of Mathematics and Physics, Xuzhou Institute of Technology, Xuzhou 221000, China
3School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China

Received 2 October 2013; Revised 15 January 2014; Accepted 3 February 2014; Published 13 March 2014

Academic Editor: Martin Ostoja-Starzewski

Copyright © 2014 Bao Wang et al. 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 strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by an infinite tree with uniformly bounded degree, which extends the corresponding results of countable Markov chains indexed by a Cayley tree and generalizes the relative results of finite Markov chains indexed by a uniformly bounded tree.