Latouche, G.; Pearce, C. E. M.; Taylor, P. G. Invariant measures for quasi-birth-and-death processes. (English) Zbl 0930.60065 Commun. Stat., Stochastic Models 14, No. 1-2, 443-460 (1998). Summary: We show that an irreducible level-independent quasi-birth-and-death process always has a matrix-geometric invariant measure. Furthermore, we give a construction for this invariant measure. The invariant measure is, of course, not summable over the state space if the process is null-recurrent or transient. When the process is level-dependent, there exists a matrix-product-form invariant measure. We discuss how this measure may be constructed. Cited in 9 Documents MSC: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) Keywords:quasi-birth-and-death processes; invariant measures PDFBibTeX XMLCite \textit{G. Latouche} et al., Commun. Stat., Stochastic Models 14, No. 1--2, 443--460 (1998; Zbl 0930.60065) Full Text: DOI