Reduced branching processes with very heavy tails
Andreas N. Lager{\aa}s, Serik Sagitov

TL;DR
This paper investigates the asymptotic behavior of reduced Markov branching processes with very heavy-tailed reproduction distributions, extending understanding beyond the well-studied critical case to new heavy-tail regimes.
Contribution
It introduces a new asymptotic pattern for the process conditioned on non-extinction under very heavy tails with Zubkov's regularity, expanding theoretical knowledge.
Findings
New asymptotic pattern identified for heavy-tailed regimes
Extended understanding of process behavior when tail index is zero
Results applicable to genealogical models in biology
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 . We turn to the case of very heavy tailed reproduction distribution assuming Zubkov's regularity condition with parameter . Our main result gives a new asymptotic pattern for the reduced branching process conditioned on non-extinction during a long time interval.
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Taxonomy
TopicsStochastic processes and statistical mechanics
