Some Comments on Quasi‐Birth‐and‐Death Processes and Matrix Measures
Holger Dette, Bettina Reuther · Journal of Probability and Statistics · 2010
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.