Equivalent properties for the bifurcating Markov chains indexed by a binary tree

Abstract

Guyon has introduced an important model of bifurcating Markov chains indexed by a binary tree taking values in general state space and studied their limit theorems, and applied these results to detect cellular aging. In this paper, we will establish some equivalent properties and a property for this Markov chains. From these properties one can find that two daughters only depend on their mother for bifurcating Markov chains indexed by a binary tree.

Keywords:

• Binary tree
• bifurcating Markov chains
• equivalent property

AMS SUBJECT CLASSIFICATION:

• 60G60

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11571142, 11601191,11971197), Youth talent cultivation project of Jiangsu University, Young science and technology talents lifting project of Jiangsu association for science and technology.