Sudden extinction of a critical branching process in random environment

dc.creatorWachtel, V. A. Vatutin V.
dc.date2008-09-05
dc.date.accessioned2026-07-07T10:00:59Z
dc.date.available2026-07-07T10:00:59Z
dc.descriptionLet $T$ be the extinction moment of a critical branching process $Z=(Z_{n},n\geq 0) $ in a random environment specified by iid probability generating functions. We study the asymptotic behavior of the probability of extinction of the process $Z$ at moment $n\to \infty$, and show that if the logarithm of the (random) expectation of the offspring number belongs to the domain of attraction of a non-gaussian stable law then the extinction occurs owing to very unfavorable environment forcing the process, having at moment $T-1$ exponentially large population, to die out. We also give an interpretation of the obtained results in terms of random walks in random environment.
dc.identifierhttps://arxiv.org/abs/0809.0986
dc.identifierhttp://arxiv.org/abs/0809.0986
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168496
dc.subjectProbability
dc.subject60J80; 60G50
dc.titleSudden extinction of a critical branching process in random environment
dc.typetext

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