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Shift techniques for Quasi-Birth and Death processes: canonical factorizations and matrix equations

Research paper by Dario A. Bini, Guy Latouche, Beatrice Meini

Indexed on: 28 Jan '16Published on: 28 Jan '16Published in: Mathematics - Numerical Analysis



Abstract

We revisit the shift technique applied to Quasi-Birth and Death (QBD) processes (He, Meini, Rhee, SIAM J. Matrix Anal. Appl., 2001) by bringing the attention to the existence and properties of canonical factorizations. To this regard, we prove new results concerning the solutions of the quadratic matrix equations associated with the QBD. These results find applications to the solution of the Poisson equation for QBDs.