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Equilibrium distributions for an open migration process

Published online by Cambridge University Press:  14 July 2016

P. Whittle
P. Whittle*
Affiliation:
University of Cambridge
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Summary

We consider a system of colonies in which migration, immigration and emigration take place according to a fairly general rule. Necessary and sufficient conditions for equilibrium are given in the theorem of Section (3). The equilibrium distribution of colony numbers is determined by Equations (7) and (9); the colony sizes are thus statistically independent in equilibrium.

Attention is also paid to the case where one colony becomes a “bottleneck” to circulation, when equilibrium changes character

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 3 , December 1968 , pp. 567 - 571
Copyright
Copyright © Applied Probability Trust 1968 

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References

Cox, D. R., and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen.Google Scholar
Whittle, P. (1967) Nonlinear migration processes. To appear in the Proceedings of the 36th Session of the International Statistical Institute.Google Scholar