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Computing approximate stationary distributions for discrete Markov processes with banded infinitesimal generators

Published online by Cambridge University Press:  14 July 2016

Carlos F. Borges  and
Craig S. Peters
Carlos F. Borges*
Affiliation:
Naval Postgraduate School, Monterey
Craig S. Peters*
Affiliation:
General Electric Co., New York
*
∗Postal address: Code MA/BC, Naval Postgraduate School, Monterey, CA 93943, USA. Email address: [email protected]
∗∗Postal address: General Electric Co., Building K1, SC1D, One Research Circle, Niskayina, NY 12309, USA.
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Abstract

We develop an algorithm for computing approximations to the stationary distribution of a discrete birth-and-death process, provided that the infinitesimal generator is a banded matrix. We begin by computing stationary distributions for processes whose infinitesimal generators are Hessenberg. Our derivation in this special case is different from the classical case but it leads to the same result. We then show how to extend these ideas to processes where the infinitesimal generator is banded (or half-banded) and to quasi-birth–death processes. Finally, we give an example of the application of this method to a nearly completely decomposable Markov chain to demonstrate the general applicability of the technique.

Keywords

Homogeneous complementsingular value decomposition
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 1086 - 1100
Copyright
Copyright © Applied Probability Trust 1999 

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