Reduced branching processes with very heavy tails

2007/10/15 by Andreas Nordvall Lagerås, Andreas N. Lagerås, Lagerås, Andreas N. +2 · 1 citation
Mathematics · #60F05 #60J80 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60F05 #msc:60J80

paper · pdf · doi:10.48550/arxiv.0710.2755

15 pages, 1 figure

arxiv created 2007/10/15 · openalex publication_date 2007/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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∈(0,1]. We turn to the case of very heavy tailed reproduction distribution α=0 assuming Zubkov's regularity condition with parameter β∈(0,∞). Our main result gives a new asymptotic pattern for the reduced branching process conditioned on non-extinction during a long time interval.

Cited by

• Small deviations for critical Galton-Watson processes with infinite variance

Related

• Uniform sampling in a structured branching population
• Upper large deviations for Branching Processes in Random Environment with heavy tails
• Parameter estimation in branching processes with almost sure extinction
• Small positive values for supercritical branching processes in random environment
• Branching Processes in Random Environments with Thresholds