Sudden extinction of a critical branching process in random environment
| dc.creator | Wachtel, V. A. Vatutin V. | |
| dc.date | 2008-09-05 | |
| dc.date.accessioned | 2026-07-07T10:00:59Z | |
| dc.date.available | 2026-07-07T10:00:59Z | |
| dc.description | Let $T$ 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.identifier | https://arxiv.org/abs/0809.0986 | |
| dc.identifier | http://arxiv.org/abs/0809.0986 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168496 | |
| dc.subject | Probability | |
| dc.subject | 60J80; 60G50 | |
| dc.title | Sudden extinction of a critical branching process in random environment | |
| dc.type | text |