The packing measure of the range of super-Brownian motion (Q971946)

The author proves that the total range of Super-Brownian motion (sBm) with quadratic branching mechanism has an exact packing measure with respect to the gauge function \(g(r)=r^4(\log\log 1/r)^{-3}\) in supercritical dimensions \(d\geq 5\). More precisely, it is shown that the total occupation measure of sBm is equal to the \(g\)-packing measure restricted to its range, up to a deterministic multiplicative constant that depends only on the space dimension \(d\).