Dette, HolgerReuther, Bettina2008-11-262008-11-262008-11-26http://hdl.handle.net/2003/2587610.17877/DE290R-3142In 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. AMS: 60J10, 42C05enBlock tridiagonal infinitesimal generatorCanonical momentMatrix measureQuasi-Birth-and-Death processSpectral measure004report