Some limit theorems for the second-order Markov chains indexed by a general infinite tree with uniform bounded degree
1 Faculty of Science, Jiangsu University, Zhenjiang, 212013, China
2 School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, China
Journal of Inequalities and Applications 2012, 2012:2 doi:10.1186/1029-242X-2012-2Published: 4 January 2012
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.