The packing measure of the range of Super-Brownian motion

The packing measure of the range of Super-Brownian motion

Thomas Duquesne

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

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.

First Page: Show

Primary Subjects: 60G57, 60J80

Secondary Subjects: 28A78

Keywords: Super-Brownian motion; Brownian Snake; range; exact packing measure

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1258380794
Digital Object Identifier: doi:10.1214/09-AOP468
Mathematical Reviews number (MathSciNet): MR2573563
Zentralblatt MATH identifier: 05708806

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