The Computation of the Mean First Passage Times for Markov Chains

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aut.embargofalseen_NZ
aut.publication.placeArXiv.orgen_NZ
aut.relation.reportnumberarXiv.1701.07781v1en_NZ
aut.researcherHunter, Jeffrey
dc.contributor.authorHunter, Jen_NZ
dc.date.accessioned2018-12-19T02:08:09Z
dc.date.available2018-12-19T02:08:09Z
dc.date.copyright2017-01-15en_NZ
dc.date.issued2017-01-15en_NZ
dc.description.abstractA survey of a variety of computational procedures for finding the mean first passage times in Markov chains is presented. The author recently developed a new accurate computational technique, an Extended GTH Procedure, Hunter (Special Matrices, 2016) similar to that developed by Kohlas (Zeit. fur Oper. Res., 1986). In addition, the author recently developed a variety of new perturbation techniques for finding key properties of Markov chains including finding the mean first passage times, Hunter (Linear Algebra and its Applications, 2016). These recently developed procedures are compared with other procedures including the standard matrix inversion technique using the fundamental matrix (Kemeny and Snell, 1960), some simple generalized matrix inverse techniques developed by Hunter (Asia Pacific J. Oper. Res., 2007), and some modifications to the FUND technique of Heyman (SIAM J Matrix Anal. and Appl., 1995). MATLAB is used to compute errors and estimate computation times when the techniques are used on some test problems that have been used in the literature together with some large sparse state-space cases. For accuracy a preference for the procedure of the author is exhibited for the test problems. However it appears that the procedure, as presented, requires longer computational times.
dc.identifier.citationarXiv:1701.07781 [math.NA]
dc.identifier.urihttps://hdl.handle.net/10292/12124
dc.publisherCornell University Libraryen_NZ
dc.relation.urihttps://arxiv.org/abs/1701.07781en_NZ
dc.rightsAuthors retain the right to place his/her publication version of the work on a personal website or institutional repository for non commercial purposes. The definitive version was published in (see Citation). The original publication is available at (see Publisher’s Version).
dc.rights.accessrightsOpenAccessen_NZ
dc.titleThe Computation of the Mean First Passage Times for Markov Chainsen_NZ
dc.typeCommissioned Report
pubs.elements-id276874
pubs.organisational-data/AUT
pubs.organisational-data/AUT/Design & Creative Technologies
pubs.organisational-data/AUT/Design & Creative Technologies/Engineering, Computer & Mathematical Sciences
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