Table of Contents Author Guidelines Submit a Manuscript
Journal of Probability and Statistics
Volume 2011 (2011), Article ID 689427, 13 pages
http://dx.doi.org/10.1155/2011/689427
Research Article

Similarity Solutions of Partial Differential Equations in Probability

Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, C.P. 6079, Succursale Centre-Ville, Montréal, QC, Canada H3C 3A7

Received 2 May 2011; Accepted 6 June 2011

Academic Editor: Shein-chung Chow

Copyright © 2011 Mario Lefebvre. 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. D. R. Cox and H. D. Miller, The Theory of Stochastic Processes, Methuen, London, UK, 1965. View at Zentralblatt MATH
  2. J. L. Doob, “A probability approach to the heat equation,” Transactions of the American Mathematical Society, vol. 80, pp. 216–280, 1955. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. F. Spitzer, “Some theorems concerning 2-dimensional Brownian motion,” Transactions of the American Mathematical Society, vol. 87, pp. 187–197, 1958. View at Google Scholar · View at Zentralblatt MATH
  4. J. G. Wendel, “Hitting spheres with Brownian motion,” The Annals of Probability, vol. 8, no. 1, pp. 164–169, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. C. Yin and R. Wu, “Hitting time and place to a sphere or spherical shell for Brownian motion,” Chinese Annals of Mathematics, vol. 20, no. 2, pp. 205–214, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. C. Yin, X. Shao, and H. Cheng, “The joint density of the hitting time and place to a circle for planar Brownian motion,” Journal of Qufu Normal University, vol. 25, no. 1, pp. 7–9, 1999. View at Google Scholar
  7. J.-L. Guilbault and M. Lefebvre, “Au sujet de l'endroit de premier passage pour des processus de diffusion bidimensionnels,” Annales des Sciences Mathématiques du Québec, vol. 25, no. 1, pp. 23–37, 2001. View at Google Scholar
  8. M. Lefebvre and J.-L. Guilbault, “Hitting place probabilities for two-dimensional diffusion processes,” Revue Roumaine de Mathématiques Pures et Appliquées, vol. 49, no. 1, pp. 11–25, 2004. View at Google Scholar · View at Zentralblatt MATH
  9. S. Karlin and H. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, NY, USA, 1981.
  10. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, NY, USA, 1965.
  11. C. H. Edwards Jr. and D. E. Penney, Elementary Differential Equations with Applications, Prentice Hall, Englewood Cliffs, NJ, USA, 1985.
  12. E. Butkov, Mathematical Physics, Addison-Wesley, Reading, Mass, USA, 1968. View at Zentralblatt MATH