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

A. C. Okoroafor

 Department of Mathematics, Abia State University, 440001 Uturu, Nigeria
Received 3 August 2007; Revised 27 May 2008; Accepted 12 August 2008

Recommended by Mohsen Pourahmadi

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.