• A comparison of computational techniques of the key properties of Markov Chains

      Hunter, JJ (Australia and New Zealand Industrial and Applied Mathematics (ANZIAM), 2015)
      The presenter has recently been exploring the accurate computation of the stationary distribution for finite Markov chains based upon the Grassman, Taksar and Heyman (GTH) algorithm ([1]) with further extensions of this ...
    • Markov Chain properties in terms of column sums of the transition matrix

      Hunter, JJ (Faculty of Mathematics and Computer Science, University of Tartu, 2012)
      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 mean first passage times and the ...
    • Markov chain properties in terms of column sums of the transition matrix

      Hunter, JJ (Victoria University of Wellington, New Zealand, 2011)
      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 mean first passage times and the ...
    • The accurate computation of key properties of Markov and semi-Markov Processes

      Hunter, JJ (The University of Melbourne, 2014)
      Based upon the Grassman, Taksar and Heyman algorithm [1] and the equivalent Sheskin State Reduction algorithm [2] for finding the stationary distribution of a finite irreducible Markov chain, Kohlas [3] developed a procedure ...
    • The derivation of Markov Chain Properties using Generalized Matrix Inverses

      Hunter, JJ (Manipal Univ Press/arXiv, 2011)
      In many stochastic models a Markov chain is present either directly or indirectly through some form of embedding. The analysis of many problems of interest associated with these models, eg. stationary distributions, moments ...
    • The distribution of Mixing Times in Markov Chains

      Hunter, JJ (arXiv, 2011)
      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 reach a state sampled from the stationary ...
    • The distribution of Mixing Times in Markov Chains

      Hunter, JJ (World Scientific Publishing Co & Operational Research Society of Singapore, 2012)
      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 reach a state sampled from the stationary ...
    • The role of Kemeny's constant in properties of Markov chains

      Hunter, JJ (MSM Conference, 2011)
      In a finite m-state irreducible Markov chain with stationary probabilities {πi} and mean first passage times mij (mean recurrence time when i = j) it was first shown, by Kemeny and Snell, that the sum, over j, of πj and ...