African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 262

Full Length Research Paper

A dimension result for polar sets of Brownian path in n-spaces

  A. C. Okoroafor1* and P. U. Uzoma2
  1Department of Mathematics, Abia State University, P. M. B. 2000, Uturu, Abia State, Nigeria. 2Department of Mathematics and Statistics, Federal Polytechnic Nekede, P. M. B. 1036, Owerri, Imo State, Nigeria.
Email: [email protected]

  •  Accepted: 13 August 2009
  •  Published: 30 September 2009

Abstract

Let T(x,r) denote the occupation measure of the ball of radius r centered at x for Brownian motion {Xr},0 < t < 1 in Rn , n > 3. We consider the set and show that for a = 0,h(r) = r2 (logr)λ, λ > 1. Moreover, E0 n Ea = ø for a > 0. We deduce that the Hausdorff dimension of  E0 is 2 for n > 3

 

Key words: Brownian motion, Hausdorff dimension, multifractal analysis, polar sets, occupation measure.

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This article is published under the terms of the Creative Commons Attribution License 4.0

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