Optimal Hölder index for density states of superprocesses with (1 + $beta$)-branching mechanism
- Fleischmann, Klaus
- Mytnik, Leonid
- Wachtel, Vitali
2010 Mathematics Subject Classification
- 60J80 60G75
- Dichotomy for density of superprocess states, Hölder continuity, optimal exponent, critical index, local unboundedness, multifractal spectrum, Hausdorff dimension
For 0 < alpha leq 2, a super-alpha-stable motion X in R^d with branching of index 1 + beta in (1,2) is considered. If d < alpha / beta, a dichotomy for the density of states X_t at fixed times t > 0 holds: the density function is locally Hölder continuous if d = 1 and alpha > 1 + beta, but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal Hölder index.