Computing approximate stationary distributions for discrete Markov processes with banded infinitesimal generators
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Authors
Borges, Carlos F.
Peters, Craig S.
Subjects
Homogeneous complement
singular value decomposition
singular value decomposition
Advisors
Date of Issue
1999
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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.
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Article
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Department
Applied Mathematics
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Citation
Journal of Applied Probability, Vol. 36, pp. 1086-1100, 1999.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.