Extinction times for a general birth, death and catastrophe process

BJ Cairns, PK Pollett

Research output: Contribution to journalArticle (Academic Journal)peer-review

12 Citations (Scopus)


The birth, death and catastrophe process is an extension of the birth-death process that incorporates the possibility of reductions in population of arbitrary size. We will consider a general form of this model, in which the transition rates are allowed to depend on the current population size in an arbitrary manner. The linear case, where the transition rates are proportional to current population size, has been studied extensively. In particular, extinction probabilities, the expected time to extinction and the distribution of the population size conditional on non-extinction (the quasi-stationary distribution) have all been evaluated explicitly. However, whilst these characteristics are of interest in the modelling and management of populations, processes with linear rate coefficients represent only a very limited class of models. We addresses this limitation by allowing for a wider range of catastrophic events. Despite this generalisation, explicit expressions can still be found for the expected extinction times.
Translated title of the contributionExtinction times for a general birth, death and catastrophe process
Original languageEnglish
Pages (from-to)1211 - 1218
Number of pages8
JournalJournal of Applied Probability
Publication statusPublished - Dec 2004

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