Similarity solutions of partial differential equations in probability

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. copyright © 2011 mario lefebvre.