Linear and Nonlinear Boundary Crossing Probabilities for Brownian Motion and Related Processes

James C. Fu, Tung-Lung Wu
2010 Journal of Applied Probability  
We propose a new method to obtain the boundary crossing probabilities or the first passage time distribution for linear and nonlinear boundaries for Brownian motion. The method also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a finite Markov chain, and the boundary crossing probability of Brownian motion is cast as the limiting probability of the finite Markov chain entering a set of absorbing
more » ... ates induced by the boundaries. Error bounds are obtained. Numerical results for various types of boundary studied in the literature are provided in order to illustrate our method.
doi:10.1239/jap/1294170519 fatcat:l7mdshs7vzcnpffpeadwejicqy