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On a triplet of exponential Brownian functionals
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Alili, Larbi, Matsumoto, Hiroyuki and Shiraishi , Tomoyuki (2001) On a triplet of exponential Brownian functionals. Séminaire de Probabilités XXXV : Lecture Notes in Mathematics, Volume 1755 . pp. 396-415. doi:10.1007/978-3-540-44671-2_27
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Official URL: http://dx.doi.org/10.1007/978-3-540-44671-2_27
Abstract
We study the three-dimensional joint distribution of a Brownian motion and the integrals of its exponential and its exponential squared from some points of view. We show an explicit expression of the Laplace transform of the distribution, which gives an extension of Yor’s resutlt on the two-dimensional one. We apply the result to some problems, in particular, to the calculation of an explicit form of the heat kernel of the semigroup generated by the Maass Laplacian on the Poincaré upper half plane.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
| Journal or Publication Title: | Séminaire de Probabilités XXXV : Lecture Notes in Mathematics | ||||
| Publisher: | Springer Berlin Heidelberg | ||||
| Official Date: | 2001 | ||||
| Dates: |
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| Volume: | Volume 1755 | ||||
| Page Range: | pp. 396-415 | ||||
| DOI: | 10.1007/978-3-540-44671-2_27 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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