Table of Contents
ISRN Optics
Volume 2012, Article ID 604074, 7 pages
http://dx.doi.org/10.5402/2012/604074
Research Article

Statistical Properties and Applications of Correlated Length Intervals of Some Stationary Random Point Processes

Laboratoire des Signaux et Systèmes, CNRS and École Supérieure d' Électricité, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette, France

Received 15 November 2011; Accepted 18 December 2011

Academic Editors: Y. Cai and J. Li

Copyright © 2012 Cherif Bendjaballah. 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

The point process, a sequence of random univariate random variables derived from correlated bivariate random variables as modeled by Arnold and Strauss, has been examined. Statistical properties of the time intervals between the points as well as the probability distributions of the number of points registered in a finite interval have been analyzed specifically in function of the coefficient of correlation. The results have been applied to binary detection and to the transmission of information. Both the probability of error and the cut-off rate have been bounded. Several simulations have been generated to illustrate the theoretical results.