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-birth-and-death processes by means of this matrixmeasure and illustrate the theoretical results by several examples. copyright © 2010 holger dette and bettina reuther.