Counterexample to a theorem on quasi-birth-and-death processes
Probability
2020-02-11 v3
Abstract
The paper disproves a basic theorem on quasi-birth-and-death processes given in [M. F. Neuts (1995). Matrix Geometric Solutions in Stochastic Models: An Algorithmic Approach. Dover, New York].
Cite
@article{arxiv.2001.07918,
title = {Counterexample to a theorem on quasi-birth-and-death processes},
author = {Vyacheslav M. Abramov},
journal= {arXiv preprint arXiv:2001.07918},
year = {2020}
}
Comments
Some time ago I read aforementioned book by M. Neuts. I noticed that existence of a least nonnegative solution to matrix equation was not justified in the sense that it should be. My attempt to build a counterexample was not successful, I was shown on errors in my arguments. Because of further increasing complexity of derivations and calculations, I decided to give up and withdraw this submission