Abstract:
Let X be a birth and death process on with absorption at zero
and suppose that X is suitably recurrent, irreducible, and
non-explosive. In a recent paper, Roberts and Jacka (1994) showed that
as
the process conditioned to non-absorption until time T
converges weakly to a time-homogeneous Markov limit,
,
which is itself a birth and death process. However the question of the
possibility of explosiveness of
remained open. The major
result of this paper establishes that
is always
non-explosive.
Keywords: Invariant measures, quasi-stationary distributions.
Acknowledgements: The research of P. Pollett was supported by the Australia Research Council (Grant No. A69130032).
The authors:
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Last modified: 21st March 1998