×

zbMATH — the first resource for mathematics

The use of packing measure in the analysis of random sets. (English) Zbl 0607.60033
Stochastic processes and their applications, Proc. Int. Conf., Nagoya/Jap. 1985, Lect. Notes Math. 1203, 214-222 (1986).
[For the entire collection see Zbl 0593.00018.]
The author and C. Tricot [Trans. Am. Math. Soc. 288, 679-699 (1985; Zbl 0537.28003)] gave the definition and properties of packing measure with respect to \(\phi\) (s), a monotone real function. Since \(\phi\)- packing measure is at least as big as Hausdorff \(\phi\)-measure, the fractal index obtained from packing measure, called the packing dimension of a set, is at least as big as the Hausdorff dimension. The present paper obtains the packing dimension of sets defined by the trajectory of a Lévy process in \({\mathbb{R}}^ n\).

MSC:
60G17 Sample path properties
28A75 Length, area, volume, other geometric measure theory
60D05 Geometric probability and stochastic geometry