The Annals of Probability

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

Klaus Fleischmann, Leonid Mytnik, and Vitali Wachtel

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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.

Article information

Ann. Probab., Volume 38, Number 3 (2010), 1180-1220.

First available in Project Euclid: 2 June 2010

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G57: Random measures

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


Fleischmann, Klaus; Mytnik, Leonid; Wachtel, Vitali. Optimal local Hölder index for density states of superprocesses with (1+ β )-branching mechanism. Ann. Probab. 38 (2010), no. 3, 1180--1220. doi:10.1214/09-AOP501.

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