The Annals of Probability

Multifractal analysis of superprocesses with stable branching in dimension one

Leonid Mytnik and Vitali Wachtel

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We show that density functions of a $(\alpha,1,\beta)$-superprocesses are almost sure multifractal for $\alpha>\beta+1$, $\beta\in(0,1)$ and calculate the corresponding spectrum of singularities.

Article information

Ann. Probab., Volume 43, Number 5 (2015), 2763-2809.

Received: January 2013
Revised: July 2014
First available in Project Euclid: 9 September 2015

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 28A80: Fractals [See also 37Fxx]
Secondary: 60G57: Random measures

Multifractal spectrum superprocess Hölder continuity Hausdorff dimension


Mytnik, Leonid; Wachtel, Vitali. Multifractal analysis of superprocesses with stable branching in dimension one. Ann. Probab. 43 (2015), no. 5, 2763--2809. doi:10.1214/14-AOP951.

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