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A note on the age-dependent branching process with immigration

Published online by Cambridge University Press:  14 July 2016

Norman Kaplan
Norman Kaplan*
Affiliation:
University of California, Berkeley
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Abstract

Let {Z(t)}t0 be an age-dependent branching process with immigration. For a general class of functions Φ(x), a necessary and sufficient condition is given for when E{Φ (Z(t))} <∞. This result is a direct generalization of a theorem proven for the branching process without immigration.

Keywords

AGE-DEPENDENT BRANCHING PROCESSIMMIGRATIONBRANCHING PROCESS WITH IMMIGRATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 130 - 134
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Athreya, K. B. (1969) On the equivalence of conditions on a branching process in continuous time and on its offspring distribution. J. Math. Kyoto Univ. 9, 41–53.Google Scholar
[2] Athreya, K. B. and Ney, P. (1972) Branching Processes. Springer-Verlag, Berlin.Google Scholar
[3] Jagers, P. (1968) Age dependent branching processes allowing immigration. Theor. Probability Appl. 13, 225–236.Google Scholar