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Path transformations of first passage bridges


Bertoin, Jean (2003). Path transformations of first passage bridges. Electronic Communications in Probability, 8:155-166.

Abstract

We define the first passage bridge from 0 to λ as the Brownian motion on the time interval [0,1] conditioned to first hit λ 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.

Abstract

We define the first passage bridge from 0 to λ as the Brownian motion on the time interval [0,1] conditioned to first hit λ 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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2003
Deposited On:26 Jun 2013 16:11
Last Modified:07 Dec 2017 21:26
Publisher:Institute of Mathematical Statistics
ISSN:1083-589X
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/ECP.v8-1096
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2042754
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1061.60083

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