Le Gall, J.-F.; Taylor, S. James The packing measure of planar Brownian motion. (English) Zbl 0619.60074 Stochastic processes, 6th Semin., Charlottesville/Va. 1986, Prog. Probab. Stat. 13, 139-147 (1987). [For the entire collection see Zbl 0607.00014.] The notion of packing measure was introduced by S. J. Taylor and C. Tricot [Trans. Am. Math. Soc. 288, 679-699 (1985; Zbl 0537.28003)], as a new tool for measuring the size of subsets of \({\mathbb{R}}^ d\). The present paper deals with the packing measure of a planar Brownian path (the case of Brownian motion in \({\mathbb{R}}^ d\), \(d\geq 3\), was treated by Taylor and Tricot). An integral test is given which determines, for every measure function f, whether the f-packing measure of the path is zero or infinite. In particular, there exists no measure function f such that the corresponding measure is both positive and finite. The proof depends on a simple representation for the local time process of a two-dimensional Bessel process. Cited in 2 Documents MSC: 60J65 Brownian motion 60J55 Local time and additive functionals 60G17 Sample path properties Keywords:occupation times of disks; packing measure; packing measure of a planar Brownian path; local time process; two-dimensional Bessel process Citations:Zbl 0607.00014; Zbl 0537.28003 PDFBibTeX XML