Haldane's asymptotics for supercritical branching processes in an iid random environment
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913620060798976 |
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| author | Boenkost, Florin Kersting, Götz |
| author_facet | Boenkost, Florin Kersting, Götz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_10684 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Haldane's asymptotics for supercritical branching processes in an iid random environment Boenkost, Florin Kersting, Götz Probability (Primary) 60J80, (Secondary) 92D25 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. |
| title | Haldane's asymptotics for supercritical branching processes in an iid random environment |
| topic | Probability (Primary) 60J80, (Secondary) 92D25 |
| url | https://arxiv.org/abs/2109.10684 |