The generalizations of strong law of large numbers for asymptotic even–odd Markov chains indexed by a homogeneous tree

Abstract

Yang et al. (Yang et al., J. Math. Anal. Appl., 410 (2014), 179–189.) have obtained the strong law of large numbers and asymptotic equipartition property for the asymptotic even–odd Markov chains indexed by a homogeneous tree. In this article, we are going to study the strong law of large numbers and the asymptotic equipartition property for a class of non homogeneous Markov chains indexed by a homogeneous tree which are the generalizations of above results. We also provide an example showing that our generalizations are not trivial.

KEYWORDS:

• Asymptotic equipartition property
• Homogeneous tree
• Non homogeneous Markov chains
• Strong law of large numbers

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15
• 60G60

Funding

This work was supported by the National Natural Science Foundation of China 11571142.