The Strong Law of Large Numbers and the Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree


Guyon (Guyon J. Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann Appl Probab, 2007, 17: 1538-1569) introduced an vital model for homogeneous bifurcating Markov chains indexed by a binary tree taking values in general state area and studied their limit theorems. The results were applied to detect cellular aging. In this paper, we outline a discrete kind of nonhomogeneous bifurcating Markov chains indexed by a binary tree and discuss the equivalent properties for them. The strong law of huge numbers and therefore the entropy ergodic theorem are studied for these Markov chains with finite state area. In contrast to previous work, we use a new approach to prove the main results of this paper.

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