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Invariant measures for quasi-birth-and-death processes. (English) Zbl 0930.60065

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.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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