Year: 2007
Type: preprint
Abstract: The reduced Markov branching process is a stochastic model for the genealogy of an unstructured biological population. Its limit behavior in the critical case is well studied for the Zolotarev-Slack regularity parameter $α\in(0,1]$. We turn to the case of very heavy tailed reproduction distribution $α=0$ assuming Zubkov's regularity condition with parameter $β\in(0,\infty)$. Our main result gives a new asymptotic pattern for the reduced branching process conditioned on non-extinction during a long time interval.
Source: arXiv (Cornell University)
Authors: Lagerås, Andreas N., Sagitov, Serik
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394658745