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 Electronic Communications in Probability > Vol. 8 (2003) > Paper 17 open journal systems 


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.


Full text: PDF

Pages: 155-166

Published on: December 17, 2003





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Electronic Communications in Probability. ISSN: 1083-589X