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A branching model by population size dependence

Published online by Cambridge University Press:  01 July 2016

Carla Lipow
Carla Lipow*
Affiliation:
University of Pittsburgh
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Abstract

A continuous-time Markov branching process is modified to allow some dependence of offspring generating function on population size. The model involves a given population size M, below which the offspring generating function is supercritical and above which it is subcritical. Immigration is allowed when the population size is 0. The process has a stationary measure, and an expression for its generating function is found. A limit theorem for the stationary measure as M tends to ∞ is then obtained.

Keywords

BRANCHING PROCESSPOPULATION GROWTHPOPULATION SIZE DEPENDENCE
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 3 , September 1975 , pp. 495 - 510
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Chung, K. L. (1967) Markov Chains with Stationary Transition Probabilities. Springer-Verlag, New York.Google Scholar
[2] Feller, W. (1966) An Introduction to Probability Theory and its Applications, Volume II. Wiley, New York.Google Scholar
[3] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
[4] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar