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| HAL : hal-00355172, version 1 |
| arXiv : 0901.3464 |
| Fiche détaillée |  Récupérer au format |
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| Excursions of the integral of the Brownian motion |
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| Emmanuel Jacob 1 |
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| (22/01/2009) |
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| The integrated Brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first construct a stationary Langevin process and then determine explicitly its stationary excursion measure. This is then used to provide new descriptions of Itô's excursion measure of the Langevin process reflected at a completely inelastic boundary, which has been introduced recently by Bertoin. |
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| 1 : | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot |
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| Domaine | : | Mathématiques/Probabilités |
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| Langevin process – stationary process – excursion measure – time-reversal – h-transform |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00355172, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00355172 | |
| oai:hal.archives-ouvertes.fr:hal-00355172 | |
| Contributeur : Emmanuel Jacob | |
| Soumis le : Jeudi 22 Janvier 2009, 12:05:02 | |
| Dernière modification le : Jeudi 22 Janvier 2009, 13:15:13 | |
