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LIMITING CONDITIONAL DISTRIBUTIONS FOR BIRTH-DEATH PROCESSES
 

Summary: LIMITING CONDITIONAL DISTRIBUTIONS FOR
BIRTH-DEATH PROCESSES
M. Kijima1
, University of Tsukuba
M.G. Nair2
, Curtin University of Technology
P.K. Pollett3
, University of Queensland
E.A. van Doorn4
, University of Twente
Abstract
In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive,
evanescent birth-death process for which absorption is certain, and established conditions for the existence
of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of
directions. We shall consider separately two cases depending on whether or not the process is evanescent. In the
former case we shall relax the condition that absorption is certain. Furthermore, we shall allow for the possibility
that the minimal process might be explosive, so that the transition rates alone will not necessarily determine
the birth-death process uniquely. Although we shall be concerned mainly with the minimal process, our most
general results hold for any birth-death process whose transition probabilities satisfy both the backward and
the forward Kolmogorov differential equations.

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering