The strong law of large numbers for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree

ABSTRACT

This article is devoted to the strong law of large numbers and the entropy ergodic theorem for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree, which generalizes the relevant results of tree-indexed nonhomogeneous bifurcating Markov chains. Meanwhile, our proof is quite different from the traditional method.

KEYWORDS:

• Entropy ergodic theorem
• M-branch Cayley tree
• Nonhomogeneous M-bifurcating Markov chains
• Strong law of large numbers

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15
• 60J10

Acknowledgments

The author would like to thank the editor and the anonymous reviewers for their valuable comments which allowed me to improve the quality of this article significantly.