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May 2010 Optimal local Hölder index for density states of superprocesses with (1+β)-branching mechanism
Klaus Fleischmann, Leonid Mytnik, Vitali Wachtel
Ann. Probab. 38(3): 1180-1220 (May 2010). DOI: 10.1214/09-AOP501


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.


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Klaus Fleischmann. Leonid Mytnik. Vitali Wachtel. "Optimal local Hölder index for density states of superprocesses with (1+β)-branching mechanism." Ann. Probab. 38 (3) 1180 - 1220, May 2010.


Published: May 2010
First available in Project Euclid: 2 June 2010

zbMATH: 1207.60055
MathSciNet: MR2674997
Digital Object Identifier: 10.1214/09-AOP501

Primary: 60J80
Secondary: 60G57

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

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 3 • May 2010
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