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On the joint law of the L-1 and L-2 norms of a 3-dimensional Bessel bridge
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Alili, Larbi and Patie, Pierre (2007) On the joint law of the L-1 and L-2 norms of a 3-dimensional Bessel bridge. Séminaire de Probabilités XL, Volume 1899 . pp. 247-264. ISSN 0075-8434.
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Official URL: http://dx.doi.org/10.1007/978-3-540-71189-6_13
Abstract
We give an analytical expression for the joint Laplace transform of the L-1 and L-2 norms of a 3-dimensional Bessel bridge. We derive the results by using merely probabilistic arguments. More precisely we show that the law of this functional is closely connected with the one of the first passage time of an Ornstein-Uhlenbeck process. The motivation for studying this problem are multiple; as an instance, they include the computation of the density of the first passage time of Brownian motion over some moving boundaries such as the square root and the quadratic ones.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
| Series Name: | Lecture Notes in Mathematics | ||||
| Journal or Publication Title: | Séminaire de Probabilités XL | ||||
| Publisher: | Springer Verlag | ||||
| ISSN: | 0075-8434 | ||||
| Official Date: | 2007 | ||||
| Dates: |
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| Volume: | Volume 1899 | ||||
| Number of Pages: | 18 | ||||
| Page Range: | pp. 247-264 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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