Supercritical general branching processes conditioned on extinction are subcritical
Probability
2007-12-13 v1
Abstract
It is well known that a simple, supercritical Bienaym\'e-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.
Keywords
Cite
@article{arxiv.0712.1872,
title = {Supercritical general branching processes conditioned on extinction are subcritical},
author = {Peter Jagers and Andreas Nordvall Lagerås},
journal= {arXiv preprint arXiv:0712.1872},
year = {2007}
}
Comments
6 pages