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On Doney’s striking factorization of the Arc-Sine Law
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Alili, Larbi, Bartholmé, Carine, Chaumont, Loïc, Patie, Pierre, Savov, Mladen and Vakeroudis, Stavros (2021) On Doney’s striking factorization of the Arc-Sine Law. In: Chaumont, L. and Kyprianou, A. E., (eds.) A Lifetime of Excursions Through Random Walks and Lévy Processes. Progress in Probability, 78 . Cham: Birkhäuser, pp. 43-58. ISBN 9783030833084
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Official URL: http://dx.doi.org/10.1007/978-3-030-83309-1_3
Abstract
In Doney (Bull Lond Math Soc 19(2):177–182, 1987), R. Doney identifies a striking factorization of the arc-sine law in terms of the suprema of two independent stable processes of the same index by an elegant random walks approximation. In this paper, we provide an alternative proof and a generalization of this factorization based on the theory recently developed for the exponential functional of Lévy processes. As a by-product, we provide some interesting distributional properties for these variables and also some new examples of the factorization of the arc-sine law.
| Item Type: | Book Item | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
| Series Name: | Progress in Probability | ||||
| Publisher: | Birkhäuser | ||||
| Place of Publication: | Cham | ||||
| ISBN: | 9783030833084 | ||||
| ISSN: | 1050-6977 | ||||
| Book Title: | A Lifetime of Excursions Through Random Walks and Lévy Processes | ||||
| Editor: | Chaumont, L. and Kyprianou, A. E. | ||||
| Official Date: | 30 July 2021 | ||||
| Dates: |
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| Volume: | 78 | ||||
| Page Range: | pp. 43-58 | ||||
| DOI: | 10.1007/978-3-030-83309-1_3 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published |
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