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The Laws of, and Conditioning with Respect to, Last Passage Times

  • Ju-Yi Yen
  • Marc Yor
Chapter
  • 1.5k Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 2088)

Abstract

Starting with some simple relationship between the law of a transient Bessel process, Brownian scaled at a last passage time γ, and the law of the Bessel process itself, the law of γ for a general transient diffusion in (0, ) is expressed in terms of the density of its semi-group, considered with respect to time. Conditioning the past of this diffusion with respect to γ = t, is shown to yield the law of the corresponding diffusion bridge of duration t. As an example, the law of the first hit of 0 by an Ornstein–Uhlenbeck process is obtained.

Keywords

Passage Time Infinitesimal Generator Uhlenbeck Process Bessel Process Area Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Ju-Yi Yen
    • 1
  • Marc Yor
    • 2
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Laboratoire de Probabilités et Modèles AléatoiresUniversité Paris VIParis CX 05France

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