The Packing Measure of the Range of Super-Brownian Motion

2008/10/31 by Thomas Duquesne, Duquesne, Thomas
Mathematics · #28A78 #60G57 #60J80 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:28A78 #msc:60G57 #msc:60J80

paper · pdf · doi:10.48550/arxiv.0810.5673

arxiv created 2008/10/31 · arxiv updated 2009/12/01

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 log1/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.

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