Abstract. Let {X(t)}t≥0 denote a Lévy process in Rd with exponent Ψ. Taylor (1986) proved that the packing dimension of the range X([0,1]) is given by the index
We provide an alternative formulation of γ' in terms of the Lévy exponent Ψ. Our formulation, as well as methods, are Fourier-analytic, and rely on the properties of the Cauchy transform. We show, through examples, some applications of our formula.
Keywords. Lévy processes, operator stable Lévy processes, packing dimension, Hausdorff dimension.
AMS Classification (2000). 60J30, 60G17, 28A80.
Support. Research supported in part by grants from the U.S. National Science Foundation.
Pre/E-Prints. This paper is available in
Davar Khoshnevisan Department of Mathematics University of Utah 155 S, 1400 E JWB 233 Salt Lake City, UT 84112-0090, U.S.A. davar@math.utah.edu |
Yimin Xiao Department of Statistics and Probability A-413 Wells Hall Michigan State University East Lansing, MI 48824, U.S.A. xiao@stt.msu.edu |
Last Update: March 7, 2007
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2002 - Davar Khoshnevisan and Yimin Xiao