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

摘要

The transition matrix, which characterizes a discrete time homogeneousMarkov 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 thestationary distribution of a transition matrix from the viewpoint of the Perron vectorof a nonnegative matrix, based on which an algorithm for the stationary distributionis proposed. The algorithm can also be used to compute the Perron root and thecorresponding Perron vector of any nonnegative irreducible matrix. Furthermore, anumerical example is given to demonstrate the validity of the algorithm.