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Jeffrey J Hunter

Publications and source records attributed to Jeffrey J Hunter.

2 recordsLinked to original sources
arXiv2018

The Computation of the Mean First Passage Times for Markov Chains

A 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.

math.NA↗
arXiv2018

Kemeny's Function for Markov Chains and Markov Renewal Processes

Extensions of Kemeny's constant, as derived for irreducible finite Markov chains in discrete time, to Markov renewal processes and Markov chains in continuous time are discussed. Three alternative Kemeny's functions and their variants are considered. Typically, they lead to a constant if and only if the mean holding times between the states in the Markov renewal process are constant. However one particular variant leads to a constant, analogous to the discrete time Markov chain result. Specifically, if the state space is finite, the weighted sum of the mean first passage times (omitting the mean return time) with the stationary probabilities associated with the continuous time semi-Markov process is a constant for any Markov renewal process. Expressions for the Kemeny's functions and the relevant constants are derived for Markov renewal processes and special cases involving continuous time Markov chains and birth and death processes.

math.PR↗