Shift techniques for Quasi-Birth and Death processes: canonical factorizations and matrix equations
Numerical Analysis
2021-01-25 v1
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.
Keywords
Cite
@article{arxiv.1601.07717,
title = {Shift techniques for Quasi-Birth and Death processes: canonical factorizations and matrix equations},
author = {Dario A. Bini and Guy Latouche and Beatrice Meini},
journal= {arXiv preprint arXiv:1601.07717},
year = {2021}
}