Path transformations of first passage bridges
Jean Bertoin, Universite Pierre et Marie Curie
Loic Chaumont, Universite Pierre et Marie Curie
Jim Pitman, University of California at Berkeley
Abstract
We define the first passage bridge from 0 to $lambda$ as the Brownian
motion on the time interval [0,1] conditioned to first hit $lambda$ 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
propose an extension of these results to certain bridges with cyclically
exchangeable increments.
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