Let ξ be a Dawson–Watanabe superprocess in ℝd such that ξt is a.s. locally finite for every t≥0. Then for d≥2 and fixed t>0, the singular random measure ξt can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the ɛ-neighborhoods of supp ξt. When d≥3, the local distributions of ξt near a hitting point can be approximated in total variation by those of a stationary and self-similar pseudo-random measure ξ̃. 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.
Publié le : 2008-11-15
Classification:
Measure-valued branching diffusions,
super-Brownian motion,
historical clusters,
local distributions,
neighborhood measures,
hitting probabilities,
Palm distributions,
self-similarity,
moment densities,
local extinction,
60G57,
60J60,
60J80
@article{1229696600,
author = {Kallenberg, Olav},
title = {Some local approximations of Dawson--Watanabe superprocesses},
journal = {Ann. Probab.},
volume = {36},
number = {1},
year = {2008},
pages = { 2176-2214},
language = {en},
url = {http://dml.mathdoc.fr/item/1229696600}
}
Kallenberg, Olav. Some local approximations of Dawson–Watanabe superprocesses. Ann. Probab., Tome 36 (2008) no. 1, pp. 2176-2214. http://gdmltest.u-ga.fr/item/1229696600/