Excursions of the integral of the Brownian motion

Abstract : 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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2009
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Submitted on : Thursday, January 22, 2009 - 12:05:02 PM
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  • HAL Id : hal-00355172, version 1
  • ARXIV : 0901.3464

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Emmanuel Jacob. Excursions of the integral of the Brownian motion. 2009. 〈hal-00355172〉

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