Haldane's asymptotics for supercritical branching processes in an iid random environment

Florin Boenkost; Götz Kersting

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arXiv · 2109.10684

Haldane's asymptotics for supercritical branching processes in an iid random environment

Florin Boenkost·Götz Kersting

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Abstract

Branching processes in a random environment are natural generalisations of Galton-Watson processes. In this paper we analyse the asymptotic decay of the survival probability for a sequence of slightly supercritical branching processes in an iid random environment, where the offspring expectation converges from above to $1$. We prove that Haldane's asymptotics, known from classical Galton-Watson processes, turns up again in the random environment case, provided that one stays away from the critical/subcritical regime. A central building block is a connection to and a limit theorem for perpetuities with asymptotically vanishing interest rates.

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BibTeX RIS

Florin Boenkost, Götz Kersting. 2021-09-22. Haldane's asymptotics for supercritical branching processes in an iid random environment. https://arxiv.org/abs/2109.10684

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