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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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2010/730543 |
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| _version_ | 1832561955925131264 |
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| author | Holger Dette Bettina Reuther |
| author_facet | Holger Dette Bettina Reuther |
| author_sort | Holger Dette |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-05b21effd07b4a43b03eeb4188b2593b |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-05b21effd07b4a43b03eeb4188b2593b2025-02-03T01:23:47ZengWileyJournal 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 |
| spellingShingle | Holger Dette Bettina Reuther Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures Journal of Probability and Statistics |
| title | 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_short | Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures |
| title_sort | some comments on quasi birth and death processes and matrix measures |
| url | http://dx.doi.org/10.1155/2010/730543 |
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