V. A. Vatutin, E. E. Dyakonova, Ya. M. Khusanbaev, “Probabilities of small deviations of a critical Galton–Watson process with infinite variance of the number of the direct descendants of particles”, Mat. Sb., 2025, Volume 216, Number 11,Pages <nobr>62

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

V. A. Vatutin^a, E. E. Dyakonova^a, Ya. M. Khusanbaev^b

^a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
^b V. I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan

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.

Keywords: Galton–Watson branching process, reduced process, most recent common ancestor.

MSC: 60F10, 60J80

Received: 03.05.2025 and 06.05.2025

DOI: 10.4213/sm10339