Journal ArticleDOI
A branching process with disasters
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In this paper, a population process is considered where particles reproduce according to an age-dependent branching process, and are subjected to disasters which occur at the epochs of an independent renewal process.Abstract:
A population process is considered where particles reproduce according to an age-dependent branching process, and are subjected to disasters which occur at the epochs of an independent renewal process. Each particle alive at the time of a disaster, survives it with probability p and the survival of any particle is assumed independent of the survival of any other particle. The asymptotic behavior of the mean of the process is determined and as a consequence, necessary and sufficient conditions are given for extinction.read more
Citations
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Birth, immigration and catastrophe processes
TL;DR: In this article, the authors consider Markov models for growth of populations subject to catastrophes and derive explicit formulas for descriptive quantities of interest when catastrophic events reduce population size by a random amount which is either geometrically, binomially or uniformly distributed.
Journal ArticleDOI
The extinction time of a birth, death and catastrophe process and of a related diffusion model
TL;DR: The distribution of the extinction time for a linear birth and death process subject to catastrophes is determined in this paper, where the authors assume that the catastrophems occur at a rate proportional to the population size and their magnitudes are random variables having an arbitrary distribution with generating function d(·).
Journal ArticleDOI
Persistence times of populations with large random fluctuations.
TL;DR: A simple model of logistic growth with additive Poisson disasters of fixed magnitude is considered and the dependence of the persistence time of a colonizing species on the parameters of the model is discussed.
Journal ArticleDOI
The extinction time of a general birth and death process with catastrophes
TL;DR: On determine la transformee de Laplace du temps jusqu'a l'extinction et on etablit certaines conditions necessaires et suffisantes.
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
An Introduction To Probability Theory And Its Applications
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Book
The Theory of Branching Processes
TL;DR: A review of the Galton and Watson mathematical model that applies probability theory to the effects of chance on the development of populations is given in this article, followed by a systematic development of branching processes, and a brief description of some of the important applications.