Packing dimension of the range of a Lévy process

Authors:
Davar Khoshnevisan and Yimin Xiao

Journal:
Proc. Amer. Math. Soc. **136** (2008), 2597-2607

MSC (2000):
Primary 60J30, 60G17, 28A80

DOI:
https://doi.org/10.1090/S0002-9939-08-09163-6

Published electronically:
March 4, 2008

MathSciNet review:
2390532

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote a Lévy process in with exponent . Taylor (1986) proved that the packing dimension of the range is given by the index

We provide an alternative formulation of in terms of the Lévy exponent . 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.

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Additional Information

**Davar Khoshnevisan**

Affiliation:
Department of Mathematics, The University of Utah, 155 S. 1400 East, Salt Lake City, Utah 84112–0090

Email:
davar@math.utah.edu

**Yimin Xiao**

Affiliation:
Department of Statistics and Probability, A-413 Wells Hall, Michigan State University, East Lansing, Michigan 48824

Email:
xiao@stt.msu.edu

DOI:
https://doi.org/10.1090/S0002-9939-08-09163-6

Keywords:
L\'evy processes,
operator stable L\'evy processes,
packing dimension,
Hausdorff dimension.

Received by editor(s):
June 21, 2006

Received by editor(s) in revised form:
January 25, 2007, and March 1, 2007

Published electronically:
March 4, 2008

Additional Notes:
This research was partially supported by a grant from the National Science Foundation

Communicated by:
Richard C. Bradley

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.