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Packing-dimension profiles and fractional Brownian motion†

Published online by Cambridge University Press:  01 July 2008

DAVAR KHOSHNEVISAN  and
YIMIN XIAO
DAVAR KHOSHNEVISAN
Affiliation:
Department of Mathematics, 155 S. 1400 E., JWB 233, University of Utah, Salt Lake City, UT 84112–0090, U.S.A. e-mail: davar@math.utah.edu URL: http://www.math.utah.edu/~davar
YIMIN XIAO
Affiliation:
Department of Statistics and Probability, A-413 Wells Hall, Michigan State University, East Lansing, MI 48824, U.S.A. e-mail: xiao@stt.msu.edu URL: http://www.stt.msu.edu/~xiaoyimi
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Abstract

In order to compute the packing dimension of orthogonal projections Falconer and Howroyd [3] have introduced a family of packing dimension profiles Dims that are parametrized by real numbers s > 0. Subsequently, Howroyd [5] introduced alternate s-dimensional packing dimension profiles P-Dims by using Caratheodory-type packing measures, and proved, among many other things, that P-DimsE = DimsE for all integers s > 0 and all analytic sets E ⊆ RN.

The aim of this paper is to prove that P-DimsE = DimsE for all real numbers s > 0 and analytic sets E ⊆ RN. This answers a question of Howroyd [5, p. 159]. Our proof hinges on establishing a new property of fractional Brownian motion.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 205 - 213
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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