Journal of Probability and Statistics
Volume 2011 (2011), Article ID 689427, 13 pages
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.


Two-dimensional diffusion processes are considered between concentric circles and in angular sectors. The aim of the paper is to compute the probability that the process will hit a given part of the boundary of the stopping region first. The appropriate partial differential equations are solved explicitly by using the method of similarity solutions and the method of separation of variables. Some solutions are expressed as generalized Fourier series.