This paper studies the regularity properties of the density of the exit measure for super-Brownian motion with (1+β)-stable branching mechanism. It establishes the continuity of the density in dimension d=2 and the unboundedness of the density in all other dimensions where the density exists. An alternative description of the exit measure and its density is also given via a stochastic integral representation. Results are applied to the probabilistic representation of nonnegative solutions of the partial differential equation Δu=u1+β.
@article{1108141725,
author = {Le Gall, Jean-Fran\c cois and Mytnik, Leonid},
title = {Stochastic integral representation and regularity of the density for the exit measure of super-Brownian motion},
journal = {Ann. Probab.},
volume = {33},
number = {1},
year = {2005},
pages = { 194-222},
language = {en},
url = {http://dml.mathdoc.fr/item/1108141725}
}
Le Gall, Jean-François; Mytnik, Leonid. Stochastic integral representation and regularity of the density for the exit measure of super-Brownian motion. Ann. Probab., Tome 33 (2005) no. 1, pp. 194-222. http://gdmltest.u-ga.fr/item/1108141725/