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Transience and recurrence of state-dependent branching processes with an immigration component

Published online by Cambridge University Press:  01 July 2016

Joshua B. Levy
Joshua B. Levy*
Affiliation:
Georgia Institute of Technology
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Abstract

We consider the following modification of an ordinary Galton–Watson branching process. If Zn = i, a positive integer, then each parent reproduces independently of one another according to the ith {P(i)k} of a countable collection of probability measures. If Zn = 0, then Zn + 1 is selected from a fixed immigration distribution. We present sufficient conditions on the means μi, the variances σ2i, and the (2 + γ)th central absolute moments β2+γ,i of the {P(i)k}'s which ensure transience of recurrence of {Zn}.

Keywords

STATE-DEPENDENT BRANCHING PROCESSIMMIGRATIONTRANSIENCERECURRENCE
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 1 , March 1979 , pp. 73 - 92
Copyright
Copyright © Applied Probability Trust 1979 

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References

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