International Journal of Stochastic Analysis
Volume 2013 (2013), Article ID 961571, 5 pages
Research Article

Some Limit Properties of the Harmonic Mean of Transition Probabilities for Markov Chains in Markovian Environments Indexed by Cayley's Trees

College of Mathematics and Information Science, Wenzhou University, Zhejiang 325035, China

Received 7 August 2013; Revised 24 October 2013; Accepted 31 October 2013

Academic Editor: Onesimo Hernandez Lerma

Copyright © 2013 Huilin Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove some limit properties of the harmonic mean of a random transition probability for finite Markov chains indexed by a homogeneous tree in a nonhomogeneous Markovian environment with finite state space. In particular, we extend the method to study the tree-indexed processes in deterministic environments to the case of random enviroments.