Markov chain properties in terms of column sums of the transition matrix

  • Jeffrey J. Hunter School of Computing and Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand
Keywords: Markov chains, stochastic matrices, column sums, stationary distributions, mean first passage times, Kemeny constant, generalized matrix inverses

Abstract

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 Kemeny constant of the associated irreducible discrete time Markov chain. Some new relationships, including some inequalities, and partial answers to the questions, are given using a special generalized matrix inverse that has not previously been considered in the literature on Markov chains.

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Published
2020-09-25
Section
Articles