English

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

R2 v1 2026-06-21T09:53:10.196Z