Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 1, Pages 29-46
doi:10.1155/S1048953391000023
The computation of stationary distributions of Markov chains through perturbations
Department of Mathematics and Statistics, Massey University, Palmerston North, New Zealand
Received 1 January 1990; Revised 1 September 1990
Copyright © 1991 Jeffery J. Hunter. 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
An algorithmic procedure for the determination of the stationary
distribution of a finite, m-state, irreducible Markov chain, that does not
require the use of methods for solving systems of linear equations, is presented.
The technique is based upon a succession of m, rank one, perturbations of the
trivial doubly stochastic matrix whose known steady state vector is updated at
each stage to yield the required stationary probability vector.