Petr Lachout (2001)
Kybernetika
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The paper presents a discussion on linear transformations of a Wiener process. The considered processes are collections of stochastic integrals of non-random functions w.r.t. Wiener process. We are interested in conditions under which the transformed process is a Wiener process, a Brownian bridge or an Ornstein –Uhlenbeck process.
R.A. Doney, Jonathan Warren, Marc Yor (1998)
Séminaire de probabilités de Strasbourg
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Loïc Chaumont, David G. Hobson, Marc Yor (2001)
Séminaire de probabilités de Strasbourg
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Michna, Zbigniew (1998)
Journal of Applied Mathematics and Stochastic Analysis
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Emmanuel Jacob (2010)
Annales de l'I.H.P. Probabilités et statistiques
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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...
Miermont, Grégory (2001)
Electronic Journal of Probability [electronic only]
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