First Passage Time of Skew Brownian Motion

Thilanka Appuhamillage, Daniel Sheldon

Published 2010-08-18, updated 2011-03-07Version 2

Nearly fifty years after the introduction of skew Brownian motion by It\^o and McKean (1963), the first passage time distribution remains unknown. In this paper, we generalize results of Pitman and Yor (2001) and Cs\'aki and Hu (2004) to derive formulae for the distribution of ranked excursion heights of skew Brownian motion. We then derive the first passage time distribution as a simple corollary.