Séminaire de Probabilités XLVI pp 359-375

Part of the Lecture Notes in Mathematics book series (LNM, volume 2123) | Cite as

On the Law of a Triplet Associated with the Pseudo-Brownian Bridge

Chapter

Abstract

We identify the distribution of a natural triplet associated with the pseudo-Brownian bridge. In particular, for B a Brownian motion and T1 its first hitting time of the level one, this remarkable law allows us to understand some properties of the process \((B_{\mathit{uT}_{1}}/\sqrt{T_{1}},\ u \leq 1)\) under uniform random sampling, a study started in (Elie, Rosenbaum, and Yor, On the expectation of normalized Brownian functionals up to first hitting times, Preprint, arXiv:1310.1181, 2013).

Keywords

Brownian motion Pseudo-Brownian bridge Bessel process Local time Hitting times Scaling Uniform sampling Mellin transform 

References

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    R. Elie, M. Rosenbaum, M. Yor, On the expectation of normalized brownian functionals up to first hitting times. arXiv preprint arXiv:1310.1181 (2013)Google Scholar
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.University Pierre et Marie Curie (Paris 6), LPMAParis cedex 05France

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