Title: Path transformations of first passage bridges
Author: Jean Bertoin and Loic Chaumont and Jim Pitman
Date: July 2003
pub: PDF
Url: http://www.stat.berkeley.edu/~pitman/643.pdf
Abstract: We define the first passage bridge from 0 to x as the Brownian 
motion on the time interval [0,1] conditioned to first hit x at time 1. We
show that this process may be related to the Brownian bridge, the
Bessel bridge or the Brownian excursion via some path
transformations, the main one being an extension of Vervaat's
transformation. We also provide an extension of these results to
certain bridges with cyclically exchangeable increments.