WIAS Preprint No. 1327, (2008)

Optimal Hölder index for density states of superprocesses with (1 + $beta$)-branching mechanism


Authors

  • Fleischmann, Klaus
  • Mytnik, Leonid
  • Wachtel, Vitali

2010 Mathematics Subject Classification

  • 60J80 60G75

Keywords

  • Dichotomy for density of superprocess states, Hölder continuity, optimal exponent, critical index, local unboundedness, multifractal spectrum, Hausdorff dimension

DOI

10.20347/WIAS.PREPRINT.1327

Abstract

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.

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