Open Access Research

Some limit theorems for the second-order Markov chains indexed by a general infinite tree with uniform bounded degree

Zhiyan Shi1*, Weiguo Yang1, Lixin Tian1 and Qingpei Zang1,2

Author Affiliations

1 Faculty of Science, Jiangsu University, Zhenjiang, 212013, China

2 School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, China

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Journal of Inequalities and Applications 2012, 2012:2 doi:10.1186/1029-242X-2012-2

Published: 4 January 2012

Abstract

In this paper, we study a convergence theorem for a finite second-order Markov chain indexed by a general infinite tree with uniformly bounded degree. Meanwhile, the strong law of large numbers (LLN) and Shannon-McMillan theorem for a finite second-order Markov chain indexed by this tree are obtained.

2000 Mathematics Subject Classification: 60F15; 60J10.

Keywords:
uniformly bounded tree; second-order Markov chain; strong law of large numbers; Shannon-McMillan theorem