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On possible rates of growth of age-dependent branching processes with immigration

Published online by Cambridge University Press:  14 July 2016

D. R. Grey
D. R. Grey*
Affiliation:
University of Sheffield
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Abstract

It is shown that if ϕ is a given function out of a large class satisfying a certain regularity condition, then a supercritical age-dependent branching process {Z(t)} exists with deterministic immigration and given life-length and family-size distributions such that Z(t)/(eat ϕ(t)) converges in probability to a non-zero constant, a being the appropriate Malthusian parameter.

As an easy corollary one discovers the asymptotic behaviour of some processes with random immigration.

Keywords

BRANCHING PROCESSAGE-DEPENDENTSUPERCRITICALIMMIGRATIONCONVERGENCE IN DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 138 - 143
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[2] Athreya, K. B., Parthasarathy, P. R. and Sankaranarayanan, G. (1974) Supercritical age-dependent branching processes with immigration. J. Appl. Prob. 11, 695–702.CrossRefGoogle Scholar