Counterexample to a theorem on quasi-birth-and-death processes

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].

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

References in corpus (1)

• Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process