%0 Journal Article
%T Optimal local H£¿lder index for density states of superprocesses with $(1+¦Â)$-branching mechanism
%A Klaus Fleischmann
%A Leonid Mytnik
%A Vitali Wachtel
%J Mathematics
%D 2008
%I arXiv
%R 10.1214/09-AOP501
%X For $0<\alpha\leq2$, a super-$\alpha$-stable motion $X$ in $\mathsf{R}^d$ with branching of index $1+\beta\in(1,2)$ is considered. Fix arbitrary $t>0$. If $d<\alpha/\beta$, a dichotomy for the density function of the measure $X_t$ holds: the density function is locally H\"{o}lder continuous if $d=1$ and $\alpha>1+\beta$ but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local H\"{o}lder index.
%U http://arxiv.org/abs/0805.3914v4