89 citations · 187 across the 9 of their papers we have counts for
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Kemeny's Function for Markov Chains and Markov Renewal Processes
Jeffrey J Hunter
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. T…
Why is Kemeny's constant a constant?
Dario Bini, Jeffrey J. Hunter, Guy Latouche +2
In their 1960 book on finite Markov chains, Kemeny and Snell established that a certain sum is invariant. The value of this sum has become known as {\it Kemeny's constant}. Various…
The Computation of Key Properties of Markov Chains via Perturbations
Jeffrey J. Hunter
Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are…
Why the Kemeny Time is a Constant
Karl Gustafson, Jeffrey J. Hunter
We present a new fundamental intuition for why the Kemeny feature of a Markov chain is a constant. This new perspective has interesting further implications
Accurate calculations of stationary distributions and mean first passage times in Markov renewal processes and Markov chains
Jeffrey J. Hunter
This article describes an accurate procedure for computing the mean first passage times of a finite irreducible Markov chain and a Markov renewal process. The method is a refinemen…
Generalized inverses of Markovian kernels in terms of properties of the Markov chain
Jeffrey J. Hunter
All one-condition generalized inverses of the Markovian kernel I - P, where P is the transition matrix of a finite irreducible Markov chain, can be uniquely specified in terms of t…
The Role of Kemeny's Constant in Properties of Markov Chains
Jeffrey J. Hunter
In a finite state irreducible Markov chain with stationary probabilities π_i and mean first passage times m_(ij) (mean recurrence time when i = j) it was first shown by Kemeny and…
The Derivation of Markov Chain Properties using Generalized Matrix Inverses
Jeffrey J. Hunter
The analysis of many problems of interest associated with Markov chains, e.g. stationary distributions, moments of first passage time distributions and moments of occupation time r…
Markov chain properties in terms of column sums of the transition matrix
Jeffrey J. Hunter
Questions are posed regarding the influence that the column sums of the transition probabilities of a stochastic matrix (with row sums all one) have on the stationary distribution,…
The Distribution of Mixing Times in Markov Chains
Jeffrey J. Hunter
The distribution of the "mixing time" or the "time to stationarity" in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reac…