Journal of Mathematical Biology

, Volume 25, Issue 3, pp 307–325

Limit theorems for the population size of a birth and death process allowing catastrophes

  • Anthony G. Pakes

DOI: 10.1007/BF00276439

Cite this article as:
Pakes, A.G. J. Math. Biology (1987) 25: 307. doi:10.1007/BF00276439


The linear birth and death process with catastrophes is formulated as a right continuous random walk on the non-negative integers which evolves in continuous time with an instantaneous jump rate proportional to the current value of the process. It is shown that distributions of the population size can be represented in terms of those of a certain Markov branching process. The ergodic theory of Markov branching process transition probabilities is then used to develop a fairly complete understanding of the behaviour of the population size of the birth-death-catastrophe process.

Key words

Branching processes Population model Limit theorems 

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Anthony G. Pakes
    • 1
  1. 1.Mathematics DepartmentThe University of Western AustraliaNedlands