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Limiting distributions for the general branching process with immigration

Published online by Cambridge University Press:  14 July 2016

S. D. Durham
S. D. Durham*
Affiliation:
University of South Carolina
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Abstract

For the general age-dependent branching process subject to an arbitrary pattern of immigration asymptotic distributions are studied in the supercritical and critical cases. In the supercritical case a new functional form is given for the limiting cumulant-generating function and in the critical case moment conditions are given under which a randomized gamma limit law prevails. The age-structure is also considered.

Keywords

AGE-DEPENDENT BRANCHING PROCESSESIMMIGRATIONFUNCTIONAL EQUATIONSLIMITING DISTRIBUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 809 - 813
Copyright
Copyright © Applied Probability Trust 1974 

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