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.

Linked References

  1. C. Bendjaballah, “Nonclassical second-order photon statistics,” Journal of Physics B, vol. 39, no. 4, pp. 783–803, 2006. View at Publisher · View at Google Scholar · View at Scopus
  2. C. Bendjaballah, “Nonclassical photon statistics,” Physical Review A, vol. 73, no. 5, Article ID 053816, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  3. C. Bendjaballah, Introduction to Photon Communication, Springer, Heidelberg, Germany, 1995.
  4. J. A. McFadden, “On the lengths of intervals in a stationary point process,” Journal of the Royal Statistical Society B, vol. 24, pp. 364–382, 1962. View at Google Scholar
  5. C. Godrèche and J. M. Luck, “Statistics of the occupation time of renewal processes,” Journal of Statistical Physics, vol. 104, no. 3-4, pp. 489–524, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. C. Bendjaballah, “Statistical properties of several models of fractional random point processes,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, pp. 3224–3236, 2011. View at Google Scholar
  7. B. C. Arnold and D. Strauss, “Bivariate distributions with exponential conditionals,” Journal of the American Statistical Association, vol. 83, pp. 522–527, 1988. View at Google Scholar
  8. S. Nadarajah and S. Kotz, “Reliability for some bivariate exponential distributions,” Mathematical Problems in Engineering, vol. 2006, pp. 1–14, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, NY, USA, 6th edition, 2000.
  10. B. Picinbono and C. Bendjaballah, “Characterization of nonclassical optical fields by photodetection statistics,” Physical Review A, vol. 71, no. 1, Article ID 013812, 12 pages, 2005. View at Publisher · View at Google Scholar
  11. Y. Yu, “Efficient simulation of a bivariate exponential conditionals distribution,” Computational Statistics and Data Analysis, vol. 52, no. 5, pp. 2273–2276, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. C. Bendjaballah and K. Hassan, “Probability of detecting a coherent optical signal in thermal noise,” Journal of the Optical Society of America A, vol. 73, pp. 1840–1843, 1983. View at Google Scholar
  13. C. W. Helstrom, Quantum Detection and Estimation Theory, Academic Press, New York, NY, USA, 1976.
  14. J. L. Massey, “Capacity, cut-off rate and coding for a direct-detection optical channel,” IEEE Transactions on Communications, vol. 29, no. 11, pp. 1615–1621, 1981. View at Google Scholar · View at Scopus