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The supercritical birth, death and catastrophe process: Limit theorems on the set of extinction. (English) Zbl 0726.60084
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:
60J80Branching processes