Electronic Communications in Probability

Path transformations of first passage bridges

Jean Bertoin, Loic Chaumont, and Jim Pitman

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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.

Article information

Electron. Commun. Probab., Volume 8 (2003), paper no. 17, 155-166.

Accepted: 17 December 2003
First available in Project Euclid: 18 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60G09: Exchangeability 60G17: Sample path properties

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Bertoin, Jean; Chaumont, Loic; Pitman, Jim. Path transformations of first passage bridges. Electron. Commun. Probab. 8 (2003), paper no. 17, 155--166. doi:10.1214/ECP.v8-1096. https://projecteuclid.org/euclid.ecp/1463608901

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