Some local approximations of Dawson--Watanabe superprocesses
| dc.creator | Kallenberg, Olav | |
| dc.date | 2009-01-19 | |
| dc.date.accessioned | 2026-07-07T12:31:36Z | |
| dc.date.available | 2026-07-07T12:31:36Z | |
| dc.description | Let $ξ$ be a Dawson--Watanabe superprocess in $\mathbb{R}^d$ such that $ξ_t$ is a.s. locally finite for every $t\geq 0$. Then for $d\geq2$ and fixed $t>0$, the singular random measure $ξ_t$ can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the $\varepsilon$-neighborhoods of $\operatorname {supp}ξ_t$. When $d\geq3$, the local distributions of $ξ_t$ near a hitting point can be approximated in total variation by those of a stationary and self-similar pseudo-random measure $\tildeξ$. By contrast, the corresponding distributions for $d=2$ are locally invariant. Further results include improvements of some classical extinction criteria and some limiting properties of hitting probabilities. Our main proofs are based on a detailed analysis of the historical structure of $ξ$. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-AOP386 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0901.2840 | |
| dc.identifier | http://arxiv.org/abs/0901.2840 | |
| dc.identifier | Annals of Probability 2008, Vol. 36, No. 6, 2176-2214 | |
| dc.identifier | doi:10.1214/07-AOP386 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216502 | |
| dc.subject | Probability | |
| dc.subject | 60G57, 60J60, 60J80 (Primary) | |
| dc.title | Some local approximations of Dawson--Watanabe superprocesses | |
| dc.type | text |