Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 503203, 10 pages
doi:10.1155/2009/503203
Research Article

Some Limit Properties of Random Transition Probability for Second-Order Nonhomogeneous Markov Chains Indexed by a Tree

Zhiyan Shi and Weiguo Yang

Faculty of Science, Jiangsu University, Zhenjiang 212013, China

Received 1 September 2009; Accepted 24 November 2009

Academic Editor: Andrei Volodin

Copyright © 2009 Zhiyan Shi and Weiguo Yang. 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.

Abstract

We study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain and a nonhomogeneous Markov chain indexed by a tree. As corollary, we obtain the property of the harmonic mean of random transition probability for a nonhomogeneous Markov chain.