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Zbl 0726.60084
Pakes, Anthony G.; Pollett, P.K.
The supercritical birth, death and catastrophe process: Limit theorems on the set of extinction. (English)
[J] Stochastic Processes Appl. 32, No.1, 161-170 (1989). ISSN 0304-4149

Summary: The stationary conditional quasi-stationary distribution of the linear birth, death and catastrophe process is shown to exist iff the decrement distribution has a finite second order moment. Conditional limit theorems for the population size are found when this moment is infinite and a regular variation condition is satisfied. The relevance of the results in this paper to the general theory of quasi-stationary distributions is discussed.

MSC 2000:: *60J80 Branching processes

Keywords: Markovian population process; Markov branching process; quasi-stationary distribution; Conditional limit theorems

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