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Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 1, Pages 29-46
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.