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dc.contributor.authorHunter, Jen_NZ
dc.date.accessioned2016-10-11T02:54:17Z
dc.date.available2016-10-11T02:54:17Z
dc.date.copyright2016-02-17en_NZ
dc.identifier.citationarXiv:1602.05247 [math.PR]
dc.identifier.urihttp://hdl.handle.net/10292/10081
dc.description.abstractComputational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of a finite irreducible Markov chain, are developed using perturbations. The derivation of these expressions involves the solution of systems of linear equations and, structurally, inevitably the inverses of matrices. By using a perturbation technique, starting from a simple base where no such derivations are formally required, we update a sequence of matrices, formed by linking the solution procedures via generalized matrix inverses and utilising matrix and vector multiplications. Four different algorithms are given, some modifications are discussed, and numerical comparisons made using a test example. The derivations are based upon the ideas outlined in Hunter, J.J., “The computation of stationary distributions of Markov chains through perturbations”, Journal of Applied Mathematics and Stochastic Analysis, 4, 29-46, (1991).en_NZ
dc.publisherarXiv, Cornell University Libraryen_NZ
dc.relation.urihttps://arxiv.org/abs/1602.05247en_NZ
dc.rightsGranting rights for arXiv to distribute an article does not preclude later copyright assignment. Authors are thus free to publish submissions that already appear on arXiv. Authors may wish to inform the journal publisher that a prior non-exclusive license exists before transferring copyright or granting a publication license. Please check the policies of any potential publication venue before uploading to arXiv. (For the policy information of many publishers, see the SHERPA/RoMEO site.)
dc.subjectMarkov chain; Stochastic matrix; Stationary distributions; Moments of first passage times; Generalized matrix inverses; Group inverse
dc.titleThe Computation of Key Properties of Markov Chains via Perturbationsen_NZ
dc.typeCommissioned Report
dc.rights.accessrightsOpenAccessen_NZ
aut.publication.placeIthaca, N.Y., U.S.A.en_NZ
aut.relation.reportnumberarXiv.1602.05247en_NZ
pubs.elements-id211995


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