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Title: A note on extinction times for the general birth, death and catastrophe process

Authors: P. Pollett, H. Zhang and B.J. Cairns

Reference: Journal of Applied Probability 44(2): 566-569.

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Abstract:

We consider a birth, death and catastrophe process where the transition rates are allowed to depend on the population size. We obtain an explicit expression for the expected time to extinction, which is valid in all cases where extinction occurs with probability 1.

Keywords. Population processes; Hitting times; Catastrophes; Zeta distribution.

Acknowledgement. The authors acknowledge the support of the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems.


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