Email this article Probabilities of small deviations of a critical Galton–Watson process with infinite variance of the number of the direct descendants of particles
- Authors: Vatutin V.A.1, Dyakonova E.E.1, Khusanbaev Y.M.2
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
- V. I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan
- Issue: Vol 216, No 11 (2025)
- Pages: 62-89
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/351335
- DOI: https://doi.org/10.4213/sm10339
- ID: 351335
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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 investigate the structure of a reduced critical Galton-Watson process.
About the authors
Vladimir Alekseevich Vatutin
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Email: vatutin@mi-ras.ru
Scopus Author ID: 6701377350
ResearcherId: Q-4558-2016
Doctor of physico-mathematical sciences, Professor
Elena Evgen'evna Dyakonova
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Email: elena@mi-ras.ru
Scopus Author ID: 6507996691
ResearcherId: Q-6278-2016
Doctor of physico-mathematical sciences, Head Scientist Researcher
Yakubdzhan Mukhamadzhanovich Khusanbaev
V. I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan
Email: yakubjank@mail.ru
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