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Interconnected population processes

Published online by Cambridge University Press:  14 July 2016

E. Renshaw*
Affiliation:
University of Edinburgh

Abstract

This paper investigates the effect of migration between two colonies each of which undergoes a simple birth and death process. Expressions are obtained for the first two moments and approximate solutions are developed for the probability generating function of the colony sizes.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1973 

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References

Adke, S. R. (1969) A birth, death and migration process. J. Appl. Prob. 6, 687691.Google Scholar
Bailey, N. T. J. (1968) Stochastic birth, death and migration processes for spatially distributed populations. Biometrika 55, 189198.Google Scholar
Bartlett, M. S. (1966) An Introduction to Stochastic Processes. (2nd edition) Cambridge University Press.Google Scholar
Bellman, R. (1953) Stability Theory of Differential Equations. McGraw-Hill, New York.Google Scholar
Davis, A. W. (1965) On the theory of birth, death and diffusion processes. J. Appl. Prob. 2, 293322.Google Scholar
Davis, A. W. (1970) Some generalisations of Bailey's birth, death and migration model. Adv. Appl. Prob. 2, 83109.CrossRefGoogle Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. 2. Wiley, New York.Google Scholar
Puri, P. S. (1968) Interconnected birth and death processes. J. Appl. Prob. 5, 334349.Google Scholar
Renshaw, E. (1972) Birth, death and migration processes. Biometrika 59, 4960.CrossRefGoogle Scholar
Usher, M. B. and Williamson, M. H. (1970) A deterministic matrix model for handling the birth, death and migration processes of spatially distributed populations. Biometrics 26, 112.CrossRefGoogle Scholar