Regular variation in the branching random walk
| dc.creator | Iksanov, Aleksander | |
| dc.creator | Polotskiy, Sergey | |
| dc.date | 2006-04-20 | |
| dc.date.accessioned | 2026-07-07T07:11:07Z | |
| dc.date.available | 2026-07-07T07:11:07Z | |
| dc.description | Let $\{\mm_n, n=0,1,...\}$ be the supercritical branching random walk starting with one initial ancestor located at the origin of the real line. For $n=0,1,...$ let $W_n$ be the moment generating function of $\mm_n$ normalized by its mean. Denote by $AW_n$ any of the following random variables: maximal function, square function, $L_1$ and a.s. limit $W$, $\su |W-W_n|$, $\su |W_{n+1}-W_n|$. Under mild moment restrictions and the assumption that $\rP\{W_1>x\}$ regularly varies at $\infty$ it is proved that $\rP\{AW_n>x\}$ regularly varies at $\infty$ with the same exponent. All the proofs given are non-analytic in the sense that these do not use Laplace-Stieltjes transforms. The result on the tail behaviour of $W$ is established in two distinct ways. | |
| dc.description | submitted | |
| dc.identifier | https://arxiv.org/abs/math/0604439 | |
| dc.identifier | http://arxiv.org/abs/math/0604439 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111634 | |
| dc.subject | Probability | |
| dc.subject | Primary: 60G42; 60J80; Secondary: 60E99 | |
| dc.title | Regular variation in the branching random walk | |
| dc.type | text |