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The Extinction Time of a Birth, Death and Catastrophe Process and of a Related Diffusion Model
P. J. Brockwell
Advances in Applied Probability
Vol. 17, No. 1 (Mar., 1985), pp. 42-52
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/1427051
Page Count: 11
You can always find the topics here!Topics: Disasters, Population size, Generating function, Population growth, Stochastic models, Laplace transformation, Radii of convergence, Emigration, Determinism, Markov processes
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The distribution of the extinction time for a linear birth and death process subject to catastrophes is determined. The catastrophes occur at a rate proportional to the population size and their magnitudes are random variables having an arbitrary distribution with generating function d(·). The asymptotic behaviour (for large initial population size) of the expected time to extinction is found under the assumption that d(·) has radius of convergence greater than 1. Corresponding results are derived for a related class of diffusion processes interrupted by catastrophes with sizes having an arbitrary distribution function.
Advances in Applied Probability © 1985 Applied Probability Trust