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Supercritical branching processes with density independent catastrophes

Published online by Cambridge University Press:  24 October 2008

D. R. Grey
D. R. Grey
Affiliation:
Department of Probability and Statistics, The University, Sheffield S3 7 RH
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Extract

A Markov branching process in either discrete time (the Galton–Watson process) or continuous time is modified by the introduction of a process of catastrophes which remove some individuals (and, by implication, their descendants) from the population. The catastrophe process is independent of the reproduction mechanism and takes the form of a sequence of independent identically distributed non-negative integer-valued random variables. In the continuous time case, these catastrophes occur at the points of an independent Poisson process with constant rate. If at any time the size of a catastrophe is at least the current population size, then the population becomes extinct. Thus in both discrete and continuous time we still have a Markov chain with stationary transition probabilities and an absorbing state at zero. Some authors use the term ‘emigration’ as an alternative to ‘catastrophe’.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 2 , September 1988 , pp. 413 - 416
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

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