Transience and recurrence of state-dependent branching processes with an immigration component
- 1 March 1979
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 11 (1) , 73-92
- https://doi.org/10.2307/1426769
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
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