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On Possible Rates of Growth of Age-Dependent Branching Processes with Immigration

D. R. Grey
Journal of Applied Probability
Vol. 13, No. 1 (Mar., 1976), pp. 138-143
DOI: 10.2307/3212674
Stable URL: http://www.jstor.org/stable/3212674
Page Count: 6
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On Possible Rates of Growth of Age-Dependent Branching Processes with Immigration
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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 familysize distributions such that Z(t)/(eα t φ (t)) converges in probability to a non-zero constant, α being the appropriate Malthusian parameter. As an easy corollary one discovers the asymptotic behaviour of some processes with random immigration.

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