The Derivation of Markov Chain Properties Using Generalized Matrix Inverses
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Hunter, Jeffrey
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Manipal Univ Press/arXiv
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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 of first passage time distributions and moments of occupation time random variables, often requires the solution of a system of linear equations involving I – P, where P is the transition matrix of a finite, irreducible, discrete time Markov chain. Generalized matrix inverses play an important role in the solution of such singular sets of equations. In this presentation we survey the application of generalized inverses to the aforementioned problems focussing primarily on Markov chains.
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Lectures on Matrix and Graph Methods, Manipal Univ Press Eds R.B. Bapat, S.Kirkland, K.M. Prasad, S. Puntanen, pp 61-89, (2012)
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This is the author's version of a paper presented at the International Workshop and Conference on Combinatorial Matrix Theory and Generalized Inverses of Matrices 02–07 & 10–11 January 2012 Department of Statistics, Manipal University, Manipal, India