Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T02:54:03.641Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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