On some basic properties of the inhomogeneous quasi-birth-and-death process
Commun. Korean Math. Soc. 1997 Vol. 12, No. 1, 177-192
Kyung Hyune Rhee, C.E.M. Pearce
Pukyong National University, University of Adelaide
Abstract : The basic theory of the quasi-birth-and-death process is extended to a process which is inhomogeneous in levels. Several key results in the standard homogeneous theory hold in a more general context than that usually stated, in particular not requiring positive recurrence. These results are subsumed under our development. The treatment is entirely probabilistic.
Keywords : $QBD$ processes, matrix-geometric solution
MSC numbers : Primary 60K25, Secondary 60J27
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