This paper establishes the continuity of the density of $(1+\beta)$-stable
super-Brownian motion $(0<\beta<1)$ for fixed times in $d=1$,
and local
unboundedness of the
density in all higher dimensions where it exists.
We also prove local unboundedness of the density
in time for a fixed spatial parameter in any dimension where the
density exists, and local unboundedness of the occupation density
(the local time)
in the spatial parameter for dimensions $d\geq2$ where the
local time
exists.
Publié le : 2003-07-14
Classification:
Super-Brownian motion,
density,
local time,
stochastic partial differential equations.,
60G57,
60G17,
60H15
@article{1055425785,
author = {Mytnik, Leonid and Perkins, Edwin},
title = {Regularity and irregularity of $\bolds{(1+\beta)}$-stable super-Brownian motion},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 1413-1440},
language = {en},
url = {http://dml.mathdoc.fr/item/1055425785}
}
Mytnik, Leonid; Perkins, Edwin. Regularity and irregularity of $\bolds{(1+\beta)}$-stable super-Brownian motion. Ann. Probab., Tome 31 (2003) no. 1, pp. 1413-1440. http://gdmltest.u-ga.fr/item/1055425785/