Path transformations of first passage bridges

Path transformations of first passage bridges

Report Number
643
Authors
Jean Bertoin and Loic Chaumont and Jim Pitman
Citation
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.

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