The packing measure of the support of super-Brownian motion

J.-F. Le Gall, E.A. Perkins and S.J. Taylor

Stochastic Processes and their Applications, 1995, vol. 59, issue 1, 1-20

Abstract: Our object is to obtain more information about the fractal properties of super-Brownian motion. For d [greater-or-equal, slanted] 2 the closed support S(Yt) of super-Brownian motion has zero Lebesgue measure and fractal dimension 2. The exact Hausdorff measure properties of S(Yt) are also known. In this paper we show that, for d [greater-or-equal, slanted] 3 there is no measure function ø such that the packing measure ø - p(S(Yt)) is finite and positive, and give an integral test which distinguishes those ø which make the packing measure 0 or +[infinity]. Incomplete results are also obtained for d = 2.

Date: 1995
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