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Some comments on quasi-birth-and-death processes and matrix measures

Author

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  • Dette, Holger
  • Reuther, Bettina

Abstract

In this paper 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 matrix measure and illustrate the theoretical results by several examples.

Suggested Citation

  • Dette, Holger & Reuther, Bettina, 2008. "Some comments on quasi-birth-and-death processes and matrix measures," Technical Reports 2008,13, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200813
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