For 0<α≤2, a super-α-stable motion X in $\mathsf{R}^{d}$ with branching of index 1+β∈(1, 2) is considered. Fix arbitrary t>0. If d<α/β, a dichotomy for the density function of the measure Xt holds: the density function is locally Hölder continuous if d=1 and α>1+β but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local Hölder index.
Publié le : 2010-05-15
Classification:
Dichotomy for density of superprocess states,
Hölder continuity,
optimal exponent,
critical index,
local unboundedness,
multifractal spectrum,
Hausdorff dimension,
60J80,
60G57
@article{1275486191,
author = {Fleischmann, Klaus and Mytnik, Leonid and Wachtel, Vitali},
title = {Optimal local H\"older index for density states of superprocesses with (1+$\beta$)-branching mechanism},
journal = {Ann. Probab.},
volume = {38},
number = {1},
year = {2010},
pages = { 1180-1220},
language = {en},
url = {http://dml.mathdoc.fr/item/1275486191}
}
Fleischmann, Klaus; Mytnik, Leonid; Wachtel, Vitali. Optimal local Hölder index for density states of superprocesses with (1+β)-branching mechanism. Ann. Probab., Tome 38 (2010) no. 1, pp. 1180-1220. http://gdmltest.u-ga.fr/item/1275486191/