Critical branching as a pure death process coming down from infinity
Artikel i vetenskaplig tidskrift, 2023

We consider the critical Galton-Watson process with overlapping generations stemming from a single founder. Assuming that both the variance of the offspring number and the average generation length are finite, we establish the convergence of the finite-dimensional distributions, conditioned on non-extinction at a remote time of observation. The limiting process is identified as a pure death process coming down from infinity.This result brings a new perspective on Vatutin's dichotomy, claiming that in the critical regime of age-dependent reproduction, an extant population either contains a large number of short-living individuals or consists of few long-living individuals.

convergence of finite-dimensional distributions

Crump-Mode-Jagers process

Vatutin's dichotomy

Sevastyanov process

Galton-Watson process with overlapping generations

Bellman-Harris process


Serik Sagitov

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Journal of Applied Probability

0021-9002 (ISSN)

Vol. 60 2 607-628 PII S0021900222000742



Sannolikhetsteori och statistik

Matematisk analys



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