Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 167453, 10 pages
http://dx.doi.org/10.1155/2012/167453
Research Article

A Numerical Algorithm on the Computation of the Stationary Distribution of a Discrete Time Homogenous Finite Markov Chain

Di Zhao,1 Hongyi Li,1 and Donglin Su2

1LMIB, School of Mathematics and System Science, Beihang University, Beijing 100191, China
2Beihang Institute of EMC Technology, Beihang University, Beijing 100191, China

Received 8 January 2012; Revised 14 March 2012; Accepted 14 March 2012

Academic Editor: Zheng-Guang Wu

Copyright © 2012 Di Zhao et al. 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

The transition matrix, which characterizes a discrete time homogeneous Markov chain, is a stochastic matrix. A stochastic matrix is a special nonnegative matrix with each row summing up to 1. In this paper, we focus on the computation of the stationary distribution of a transition matrix from the viewpoint of the Perron vector of a nonnegative matrix, based on which an algorithm for the stationary distribution is proposed. The algorithm can also be used to compute the Perron root and the corresponding Perron vector of any nonnegative irreducible matrix. Furthermore, a numerical example is given to demonstrate the validity of the algorithm.