The Annals of Probability

The packing measure of the range of Super-Brownian motion

Thomas Duquesne

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Abstract

We prove that the total range of Super-Brownian motion with quadratic branching mechanism has an exact packing measure with respect to the gauge function g(r)=r4(log log 1/r)−3 in super-critical dimensions d≥5. More precisely, we prove that the total occupation measure of Super-Brownian motion is equal to the g-packing measure restricted to its range, up to a deterministic multiplicative constant that only depends on space dimension d.

Article information

Source
Ann. Probab., Volume 37, Number 6 (2009), 2431-2458.

Dates
First available in Project Euclid: 16 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.aop/1258380794

Digital Object Identifier
doi:10.1214/09-AOP468

Mathematical Reviews number (MathSciNet)
MR2573563

Zentralblatt MATH identifier
1191.60096

Subjects
Primary: 60G57: Random measures 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 28A78: Hausdorff and packing measures

Keywords
Super-Brownian motion Brownian Snake range exact packing measure

Citation

Duquesne, Thomas. The packing measure of the range of Super-Brownian motion. Ann. Probab. 37 (2009), no. 6, 2431--2458. doi:10.1214/09-AOP468. https://projecteuclid.org/euclid.aop/1258380794


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