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The supercritical birth, death and catastrophe process: limit theorems on the set of extinction

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  • Pakes, Anthony G.
  • Pollett, P. K.

Abstract

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

Suggested Citation

  • Pakes, Anthony G. & Pollett, P. K., 1989. "The supercritical birth, death and catastrophe process: limit theorems on the set of extinction," Stochastic Processes and their Applications, Elsevier, vol. 32(1), pages 161-170, June.
    • Handle: RePEc:eee:spapps:v:32:y:1989:i:1:p:161-170
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    Cited by:

    1. Hermann, Felix & Pfaffelhuber, Peter, 2020. "Markov branching processes with disasters: Extinction, survival and duality to p-jump processes," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2488-2518.

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