Some boundary-crossing results for linear diffusion processes

Abstract

We evaluate some boundary-crossing time density functions for time-changed Brownian motion. As examples, we evaluate the first passage time densities of Ornstein-Uhlenbeck process to exponential boundaries and Brownian bridge to two linearly shrinking boundaries. We also evaluate explicitly the first and last passage time distributions of Brownian motion for two linear boundaries. (C) 2003 Elsevier Science B.V. All rights reserved.