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Probabilities of small deviations of a critical Galton-Watson process with infinite variance of the number of the direct descendants of particles

Vladimir VatutinSteklov Mathematical Institute of Russian Academy of Sciences, Moscow, RussiaElena Evgen'evna DyakonovaSteklov Mathematical Institute of Russian Academy of Sciences, Moscow, RussiaYakubdzhan Mukhamadzhanovich KhusanbaevV. I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan
Sbornik Mathematicsjournal2025en
ABI

Abstract

We study the asymptotic behaviour of small deviation probabilities for a critical Galton-Watson process with infinite variance of the offspring sizes of particles and apply the result obtained to investigating the structure of a reduced critical Galton-Watson process under the assumption that the original process has a small deviation. Bibliography: 24 titles.

Topics

Stochastic processes and statistical mechanicsRandom Matrices and ApplicationsProbability and Risk Models

Identifiers

DOI
10.4213/sm10339e

Citations and references

Cited by 019 references
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