Electronic Journal of Probability

On the expectation of normalized Brownian functionals up to first hitting times

Romuald Elie, Mathieu Rosenbaum, and Marc Yor

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 37, 23 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065679

Digital Object Identifier
doi:10.1214/EJP.v19-3049

Mathematical Reviews number (MathSciNet)
MR3194736

Zentralblatt MATH identifier
1291.60164

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60J55: Local time and additive functionals 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Brownian motion hitting times scaling random sampling Bessel process Brownian meander Ray-Knight theorem Feynman-Kac formula

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Elie, Romuald; Rosenbaum, Mathieu; Yor, Marc. On the expectation of normalized Brownian functionals up to first hitting times. Electron. J. Probab. 19 (2014), paper no. 37, 23 pp. doi:10.1214/EJP.v19-3049. https://projecteuclid.org/euclid.ejp/1465065679


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