Branching processes in random environment die slowly
| dc.creator | Vatutin, V. | |
| dc.creator | Kyprianou, A. E. | |
| dc.date | 2008-04-07 | |
| dc.date.accessioned | 2026-07-07T09:30:59Z | |
| dc.date.available | 2026-07-07T09:30:59Z | |
| dc.description | Let $Z_{n,}n=0,1,...,$ be a branching process evolving in the random environment generated by a sequence of iid generating functions $% f_{0}(s),f_{1}(s),...,$ and let $S_{0}=0,S_{k}=X_{1}+...+X_{k},k\geq 1,$ be the associated random walk with $X_{i}=\log f_{i-1}^{\prime}(1),$ $τ(m,n)$ be the left-most point of minimum of $\left\{S_{k},k\geq 0\right\} $ on the interval $[m,n],$ and $T=\min \left\{k:Z_{k}=0\right\} $. Assuming that the associated random walk satisfies the Doney condition $P(S_{n}>0) \to ρ\in (0,1),n\to \infty ,$ we prove (under the quenched approach) conditional limit theorems, as $n\to \infty $, for the distribution of $Z_{nt},$ $Z_{τ(0,nt)},$ and $Z_{τ(nt,n)},$ $t\in (0,1),$ given $T=n$. It is shown that the form of the limit distributions essentially depends on the location of $τ(0,n)$ with respect to the point $nt.$ | |
| dc.identifier | https://arxiv.org/abs/0804.1155 | |
| dc.identifier | http://arxiv.org/abs/0804.1155 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158302 | |
| dc.subject | Probability | |
| dc.title | Branching processes in random environment die slowly | |
| dc.type | text |