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

Holger Dette and Bettina Reuther

No 2008,13, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

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.

Keywords: Block tridiagonal infinitesimal generator; Quasi-Birth-and-Death processes; spectral measure; matrix measure; canonical moments (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb475:200813

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