Some Comments on Quasi-Birth-and-Death Processes and Matrix Measures

Abstract EN

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.