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This article is cited in 24 scientific papers (total in 24 papers)
Conditional limit theorems for intermediately subcritical branching processes in random environment
V. I. Afanasyeva, Ch. Böinghoffb, G. Kerstingb, V. A. Vatutina a Department of Discrete Mathematics, Steklov Mathematical Institute, 8 Gubkin Street, 119 991 Moscow, Russia
b Fachbereich Mathematik, Universität Frankfurt, Fach 187, D-60054 Frankfurt am Main, Germany
Abstract:
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in
a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition appears. In
this paper we study the intermediately subcritical case, which constitutes the borderline within this phase transition. We study the
asymptotic behavior of the survival probability. Next the size of the population and the shape of the random environment conditioned
on non-extinction is examined. Finally we show that conditioned on non-extinction periods of small and large population
sizes alternate. This kind of ‘bottleneck’ behavior appears under the annealed approach only in the intermediately subcritical case.
Received: 13.01.2012 Revised: 18.09.2012 Accepted: 24.09.2012
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