The definition of tree-indexed Markov chains in random environment and their existence

ABSTRACT

This paper gives the definition of tree-indexed Markov chains in random environment with discrete state space, and then studies some equivalent theorems of tree-indexed Markov chains in random environment. Finally, we give the equivalence on tree-indexed Markov chains in Markov environment and double Markov chains indexed by a tree.

KEYWORDS:

• Markov chains
• random environment
• tree-indexed

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15
• 60J10

Acknowledgments

This work is supported by the National Natural Science Foundation of China [grant number 11601191], [grant number 11571142]; Research Foundation for Advanced Talents of Jiangsu University [grant number 11JDG116]; Statistic Application Research Base of The Education Department of Jiangsu Province; and The Key Discipline of Statistic of Jiangsu University in 2014.