Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures

Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures

We explore the relation between matrix measures and quasi-birth-and-death processes. We derive an integral representation of the transition function in terms of a matrix-valued spectral measure and corresponding orthogonal matrix polynomials. We characterize several stochastic properties of quasi-bi...

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Main Authors: Holger Dette, Bettina Reuther
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2010/730543
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spelling doaj-05b21effd07b4a43b03eeb4188b2593b2020-11-24T22:09:13ZengHindawi LimitedJournal of Probability and Statistics1687-952X1687-95382010-01-01201010.1155/2010/730543730543Some Comments on Quasi-Birth-and-Death Processes and Matrix MeasuresHolger Dette0Bettina Reuther1Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, GermanyFakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, GermanyWe explore the relation between matrix measures and quasi-birth-and-death processes. We derive an integral representation of the transition function in terms of a matrix-valued spectral measure and corresponding orthogonal matrix polynomials. We characterize several stochastic properties of quasi-birth-and-death processes by means of this matrixmeasure and illustrate the theoretical results by several examples.http://dx.doi.org/10.1155/2010/730543
collection DOAJ
language English
format Article
sources DOAJ
author Holger Dette
Bettina Reuther
spellingShingle Holger Dette
Bettina Reuther
Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures
Journal of Probability and Statistics
author_facet Holger Dette
Bettina Reuther
author_sort Holger Dette
title Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures
title_short Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures
title_full Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures
title_fullStr Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures
title_full_unstemmed Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures
title_sort some comments on quasi-birth-and-death processes and matrix measures
publisher Hindawi Limited
series Journal of Probability and Statistics
issn 1687-952X
1687-9538
publishDate 2010-01-01
description We explore the relation between matrix measures and quasi-birth-and-death processes. We derive an integral representation of the transition function in terms of a matrix-valued spectral measure and corresponding orthogonal matrix polynomials. We characterize several stochastic properties of quasi-birth-and-death processes by means of this matrixmeasure and illustrate the theoretical results by several examples.
url http://dx.doi.org/10.1155/2010/730543
work_keys_str_mv AT holgerdette somecommentsonquasibirthanddeathprocessesandmatrixmeasures
AT bettinareuther somecommentsonquasibirthanddeathprocessesandmatrixmeasures
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