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

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

Phil Pollett, Hanjun Zhang, and Benjamin J. Cairns

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

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.

Primary Subjects: 60J27

Secondary Subjects: 60J35

Keywords: Population process; hitting time; catastrophe; zeta distribution

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jap/1183667423
Digital Object Identifier: doi:10.1239/jap/1183667423
Mathematical Reviews number (MathSciNet): MR2340220

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References

Brockwell, P. (1985). The extinction time of a birth, death and catastrophe process and of a related diffusion model. Adv. Appl. Prob. 17, 42--52.

Mathematical Reviews (MathSciNet): MR778592

Digital Object Identifier: doi:10.2307/1427051

JSTOR: links.jstor.org

Cairns, B. and Pollett, P. (2004). Extinction times for a general birth, death and catastrophe process. J. Appl. Prob. 41, 1211--1218.

Mathematical Reviews (MathSciNet): MR2122816

Digital Object Identifier: doi:10.1239/jap/1101840567

Project Euclid: euclid.jap/1101840567

Harris, T. (1963). The Theory of Branching Processes. Springer, Berlin.

Mathematical Reviews (MathSciNet): MR163361

Zentralblatt MATH: 0117.13002

Malamud, B. D., Morein, G. and Turcotte, D. L. (1998). Forest fires: an example of self-organized critical behaviour. Science 281, 1840--1842.

Pakes, A. G. (1987). Limit theorems for the population size of a birth and death process allowing catastrophes. J. Math. Biol. 25, 307--325.

Mathematical Reviews (MathSciNet): MR900324

Digital Object Identifier: doi:10.1007/BF00276439

Pakes, A. G. and Pollett, P. K. (1989). The supercritical birth, death and catastrophe process: limit theorems on the set of extinction. Stoch. Process. Appl. 32, 161-170.

Mathematical Reviews (MathSciNet): MR1008915

Digital Object Identifier: doi:10.1016/0304-4149(89)90060-4

Pollett, P. (2001). Quasi-stationarity in populations that are subject to large-scale mortality or emigration. Environ. Internat. 27, 231--236.

Yang, Y. (1973). Asymptotic properties of the stationary measure of a Markov branching process. J. Appl. Prob. 10, 447--450.

Mathematical Reviews (MathSciNet): MR353479

Digital Object Identifier: doi:10.2307/3212362

JSTOR: links.jstor.org

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