Institute of Natural and Mathematical Sciences
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Item Stationary distributions and mean first passage times of perturbed Markov chains(Massey University, 2002) Hunter, Jeffrey J.Stationary distributions of perturbed finite irreducible discrete time Markov chains are intimately connected with the behaviour of associated mean first passage times. This interconnection is explored through the use of generalized matrix inverses. Some interesting qualitative results regarding the nature of the relative and absolute changes to the stationary probabilities are obtained together with some improved bounds.Item Generalized inverses, stationary distributions and mean first passage times with applications to perturbed Markov chains(Massey University, 2002) Hunter, Jeffrey J.In an earlier paper (Hunter, 2002) it was shown that mean first passage times play an important role in determining bounds on the relative and absolute differences between the stationary probabilities in perturbed finite irreducible discrete time Markov chains. Further when two perturbations of the transition probabilities in a single row are carried out the differences between the stationary probabilities in the unperturbed and perturbed situations are easily expressed in terms of a reduced number of mean first passage times. Using this procedure we provide an updating procedure for mean first passage times to determine changes in the stationary distributions under successive perturbations. Simple procedures for determining both stationary distributions and mean first passage times in a finite irreducible Markov chain are also given. The techniques used in the paper are based upon the application of generalized matrix inverses.