Small deviations for critical Galton-Watson processes with infinite variance

Vladimir Vatutin; Elena Dyakonova; Yakubdjan Khusanbaev

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arXiv · 2505.10137

Small deviations for critical Galton-Watson processes with infinite variance

Vladimir Vatutin·Elena Dyakonova·Yakubdjan Khusanbaev

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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.

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Vladimir Vatutin, Elena Dyakonova, Yakubdjan Khusanbaev. 2025-05-15. Small deviations for critical Galton-Watson processes with infinite variance. https://arxiv.org/abs/2505.10137

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