Table of Contents
International Journal of Statistical Mechanics
Volume 2013, Article ID 831390, 9 pages
http://dx.doi.org/10.1155/2013/831390
Research Article

Solution and Analysis of a One-Dimensional First-Passage Problem with a Nonzero Halting Probability

Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo, Tokyo 112-8551, Japan

Received 24 April 2013; Accepted 9 September 2013

Academic Editor: Michel Droz

Copyright © 2013 Ken Yamamoto. 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. S. Redner, A Guide to First-Passage Processes, Cambridge University Press, Cambridge, UK, 2001.
  2. P. Hänggi, “Reaction-rate theory: fifty years after Kramers,” Reviews of Modern Physics, vol. 62, no. 2, pp. 251–341, 1990. View at Publisher · View at Google Scholar
  3. T. Verechtchaguina, I. M. Sokolov, and L. Schimansky-Geier, “First passage time densities in resonate-and-fire models,” Physical Review E, vol. 73, no. 3, Article ID 031108, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. N. Sazuka, J.-I. Inoue, and E. Scalas, “The distribution of first-passage times and durations in FOREX and future markets,” Physica A, vol. 388, no. 14, pp. 2839–2853, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. W. Feller, An Introduction to Probability Theory and Its Applications, vol. 1, Wiley, New York, NY, USA, 1957.
  6. D. Stanton and D. White, Constructive Combinatorics, Springer, New York, NY, USA, 1986.
  7. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 1970.
  8. M. C. K. Tweedie, “Statistical properties of inverse Gaussian distributions,” Annals of Mathematical Statistics, vol. 28, pp. 362–377, 1957. View at Publisher · View at Google Scholar
  9. K. Nagel and M. Paczuski, “Emergent traffic jams,” Physical Review E, vol. 51, no. 4, pp. 2909–2918, 1995. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Gil, J. Segura, and N. M. Temme, Numerical Methods for Special Functions, SIAM, Philadelphia, Pa, USA, 2007.