Table of Contents
ISRN Discrete Mathematics
Volume 2011, Article ID 346503, 15 pages
http://dx.doi.org/10.5402/2011/346503
Research Article

First Hitting Problems for Markov Chains That Converge to a Geometric Brownian Motion

1Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, C.P. 6079, Succursale Centre-Ville, Montréal, QC, Canada H3C 3A7
2Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, QC, Canada H3C 3J7

Received 1 July 2011; Accepted 21 July 2011

Academic Editors: C.-K. Lin and B. Zhou

Copyright Β© 2011 Mario Lefebvre and Moussa Kounta. 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. M. Lefebvre, Applied Stochastic Processes, Springer, New York, NY, USA, 2007.
  2. D. R. Cox and H. D. Miller, The Theory of Stochastic Processes, Methuen, London, UK, 1965.
  3. M. Lefebvre, β€œFirst passage problems for asymmetric Wiener processes,” Journal of Applied Probability, vol. 43, no. 1, pp. 175–184, 2006. View at Publisher Β· View at Google Scholar
  4. M. Abundo, β€œFirst-passage problems for asymmetric diffusions and skew-diffusion processes,” Open Systems and Information Dynamics, vol. 16, no. 4, pp. 325–350, 2009. View at Publisher Β· View at Google Scholar
  5. M. Lefebvre and J.-L. Guilbault, β€œFirst hitting place probabilities for a discrete version of the Ornstein-Uhlenbeck process,” International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 909835, 12 pages, 2009. View at Publisher Β· View at Google Scholar
  6. J.-L. Guilbault and M. Lefebvre, β€œOn a non-homogeneous difference equation from probability theory,” Tatra Mountains Mathematical Publications, vol. 43, pp. 81–90, 2009. View at Google Scholar
  7. S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, NY, USA, 1981.