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2014 On the expectation of normalized Brownian functionals up to first hitting times
Romuald Elie, Mathieu Rosenbaum, Marc Yor
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Electron. J. Probab. 19: 1-23 (2014). DOI: 10.1214/EJP.v19-3049

Abstract

Let $B$ be a Brownian motion and $T_1$ its first hitting time of the level $1$. For $U$ a uniform random variable independent of $B$, we study in depth the distribution of $B_{UT_1}/\sqrt{T_1}$, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered.

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Romuald Elie. Mathieu Rosenbaum. Marc Yor. "On the expectation of normalized Brownian functionals up to first hitting times." Electron. J. Probab. 19 1 - 23, 2014. https://doi.org/10.1214/EJP.v19-3049

Information

Accepted: 29 March 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1291.60164
MathSciNet: MR3194736
Digital Object Identifier: 10.1214/EJP.v19-3049

Subjects:
Primary: 60J65
Secondary: 60G40, 60J55

JOURNAL ARTICLE
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Vol.19 • 2014
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