Reprint:
Packing-Dimension Profiles and Fractional Brownian Motion
D. Khoshnevisan and Yimin Xiao
Abstract.
In order to compute the packing dimension of orthogonal projections
Falconer and Howroyd (1997) introduced a family of
packing dimension profiles Dims that are parametrized by
real numbers s>0. Subsequently,
Howroyd (2001) introduced alternate s-dimensional
packing dimension profiles P-Dims and proved,
among many other things, that P-Dims E= Dims E
for all integers s>0 and all analytic sets E ⊂ RN.
The goal of this article is to prove that
P-Dims E=Dims E for all real numbers
s>0 and analytic sets E ⊂ RN.
This answers a question of Howroyd (2001, p. 159).
Our proof hinges on a new property of fractional Brownian motion.
Keywords.
Packing dimension, dimension profiles, fractional Brownian motion
AMS Classification (2000)
Primary. 60G15
Secondary. 60G17; 28A80.
Support. Research supported in part by a grant from
the 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 Halls
Michigan State University
East Lansing MI 48824
xiao@stt.msu.edu
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Last Update: November 13, 2006
© 2006 - Davar Khoshnevisan and Yimin Xiao