Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 564601, 7 pages
doi:10.1155/2008/564601
Research Article
The Packing Measure of the Trajectory of a One-Dimensional Symmetric Cauchy Process
Department of Mathematics, Abia State University, 440001 Uturu, Nigeria
Received 3 August 2007; Revised 27 May 2008; Accepted 12 August 2008
Academic Editor: Mohsen Pourahmadi
Copyright © 2008 A. C. Okoroafor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let Xt={X(t), t≥0} be a one-dimensional symmetric Cauchy process. We prove that, for any measure function, φ,φ−p(X[0,τ]) is zero or infinite, where φ−p(E) is the φ-packing measure of E, thus solving a problem posed by Rezakhanlou and Taylor in 1988.