Transformation on diffusion processes and first passage time to the moving boundaries

Abstract

In this paper, we study the first passage time of a diffusion process to a moving boundary. Under some special conditions we apply a transformation to diffusion process and to the boundary function and then in each case obtain the first passage time distribution of the original process by the first passage time distribution of transformed process to transformed boundary. In addition, by applying these transformations to the Ornstein- Uhlenbeck and Wiener processes the first passage time distributions for the new boundaries are presented as examples.