The Packing Measure of the Range of Super-Brownian Motion

Details The Packing Measure of the Range of Super-Brownian Motion The Packing Measure of the Range of Super-Brownian Motion

2008-10-31

arxiv.org/abs/0810.5673v1

Mathematics

Probability

Scientific paper

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 $g(r)=r^4 (\log \log1/r)^{-3}$ in super-critical dimensions $d\geq 5$. 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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