Bertoin, Jean (2003). Path transformations of first passage bridges. Electronic Communications in Probability, 8:155-166.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty |
| Language: | English |
| Date: | 2003 |
| Deposited On: | 26 Jun 2013 16:11 |
| Last Modified: | 10 Nov 2023 02:38 |
| Publisher: | Institute of Mathematical Statistics |
| ISSN: | 1083-589X |
| OA Status: | Gold |
| 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 |
Bertoin, Jean