Journal of Applied Probability

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

Phil Pollett, Hanjun Zhang, and Benjamin J. Cairns

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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.

Article information

Source
J. Appl. Probab. Volume 44, Number 2 (2007), 566-569.

Dates
First available in Project Euclid: 5 July 2007

Permanent link to this document
http://projecteuclid.org/euclid.jap/1183667423

Digital Object Identifier
doi:10.1239/jap/1183667423

Mathematical Reviews number (MathSciNet)
MR2340220

Zentralblatt MATH identifier
1154.60064

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Keywords
Population process hitting time catastrophe zeta distribution

Citation

Pollett, Phil; Zhang, Hanjun; Cairns, Benjamin J. A note on extinction times for the general birth, death and catastrophe process. J. Appl. Probab. 44 (2007), no. 2, 566--569. doi:10.1239/jap/1183667423. http://projecteuclid.org/euclid.jap/1183667423.


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References

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