General branching processes conditioned on extinction are still branching processes
Peter Jagers, Chalmers University of Technology and University of Gothenburg
Andreas Nordvall Lagerås, Department of Mathematics, Stockholm University
Abstract
It is well known that a simple, supercritical
Bienaymé-Galton-Watson process turns into a subcritical such
process, if conditioned to die out. We prove that the corresponding
holds true for general, multi-type branching, where child-bearing
may occur at different ages, life span may depend upon reproduction,
and the whole course of events is thus affected by conditioning upon
extinction.
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