The Derivation of Markov Chain Properties using Generalized Matrix Inverses

Details The Derivation of Markov Chain Properties using Generalized Matrix Inverses The Derivation of Markov Chain Properties using Generalized Matrix Inverses

2011-12-15

arxiv.org/abs/1112.3404v1

Mathematics

Probability

31 pages

Scientific paper

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 random variables, involves 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 inverses play an important role in the solution of such singular sets of equations. In this presentation we survey the application of generalized matrix inverses to the aforementioned problems.

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