Generalized inverses, stationary distributions and mean first passage times with applications to perturbed Markov chains
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Date
2002
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Massey University
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Abstract
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.
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Keywords
Markov chains, Perturbation theory, First passage time, Stochastic process, Generalized inverse, Stationary distribution
Citation
Hunter, J.J. (2002), Generalized inverses, stationary distributions and mean first passage times with applications to perturbed Markov chains, Research Letters in the Information and Mathematical Sciences, 3, 99-116