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.
Yimin Xiao
Department of Statistics and Probability
A-413 Wells Halls
Michigan State University
East Lansing MI 48824

Last Update: November 13, 2006
© 2006 - Davar Khoshnevisan and Yimin Xiao