Small deviations for critical Galton-Watson processes with infinite variance

TL;DR

This paper investigates the asymptotic probabilities of small deviations in critical Galton-Watson processes with infinite variance, providing insights into their structure and behavior.

Contribution

It introduces new asymptotic results for small deviations in critical Galton-Watson processes with infinite variance, enhancing understanding of their probabilistic structure.

Findings

Derived asymptotic formulas for small deviation probabilities.

Analyzed the structure of reduced critical Galton-Watson processes.

Extended results to processes with infinite variance offspring distributions.

Abstract

We study the asymptotic behavior of small deviation probabilities for the critical Galton-Watson processes with infinite variance of the offspring sizes of particles and apply the obtained result to investigate the structure of a reduced critical Galton-Watson process.