arXiv:2505.10137 Abstract | arXiv Analytics

arXiv:2505.10137 [math.PR]Abstract References Reviews Resources

Small deviations for critical Galton-Watson processes with infinite variance

Vladimir Vatutin, Elena Dyakonova, Yakubdjan Khusanbaev

Published 2025-05-15Version 1

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.

Comments: 30 pages

Categories: math.PR

Subjects: 60J80, 60F10

Keywords: infinite variance, small deviation probabilities, asymptotic behavior, reduced critical galton-watson process, offspring sizes

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