Journal of Applied Mathematics and Stochastic Analysis
Volume 2007 (2007), Article ID 81934, 9 pages
Research Article

Some Local Asymptotic Laws for the Cauchy Process on the Line

A. Chukwuemeka Okoroafor

Department of Mathematics, Abia State University, Uturu, Nigeria

Received 22 September 2006; Revised 19 January 2007; Accepted 9 May 2007

Copyright © 2007 A. Chukwuemeka 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.


This paper investigates the lim inf behavior of the sojourn time process and the escape rate process associated with the Cauchy process on the line. The monotone functions associated with the lower asymptotic growth rate of the sojourn time are characterized and the asymptotic size of the large values of the escape rate process is developed.