Critical branching processes in a sparse random environment

Dariusz Buraczewski; Congzao Dong; Alexander Iksanov; Alexander Marynych

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arXiv · 2306.06730

Critical branching processes in a sparse random environment

Dariusz Buraczewski·Congzao Dong·Alexander Iksanov·Alexander Marynych

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Abstract

We introduce a branching process in a sparse random environment as an intermediate model between a Galton--Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and prove Yaglom-type limit theorems, that is, limit theorems for the size of population conditioned on the survival event.

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Dariusz Buraczewski, Congzao Dong, Alexander Iksanov, Alexander Marynych. 2023-06-11. Critical branching processes in a sparse random environment. https://arxiv.org/abs/2306.06730

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