Some comments on quasi-birth-and-death processes and matrix measures - Holger Dette; Bettina Reuther (Technische Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2008)
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: 519; Block tridiagonal infinitesimal generator; Quasi-Birth-and-Death processes; spectral measure; matrix measure; canonical moments