## Electronic Communications in Probability

### Path transformations of first passage bridges

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.ecp/1463608901

Digital Object Identifier
doi:10.1214/ECP.v8-1096

Mathematical Reviews number (MathSciNet)
MR2042754

Zentralblatt MATH identifier
1061.60083

Subjects
Secondary: 60G09: Exchangeability 60G17: Sample path properties

Rights

#### Citation

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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