Electronic Journal of Probability

The Maximum of Brownian Motion Minus a Parabola

Piet Groeneboom

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Abstract

We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of the distribution, both for one-sided and two-sided Brownian motion.

Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 62, 1930-1937.

Dates
Accepted: 17 November 2010
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819847

Digital Object Identifier
doi:10.1214/EJP.v15-826

Mathematical Reviews number (MathSciNet)
MR2738343

Zentralblatt MATH identifier
1226.60110

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60J75: Jump processes

Keywords
Brownian motion parabolic drift maximum Airy functions

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Groeneboom, Piet. The Maximum of Brownian Motion Minus a Parabola. Electron. J. Probab. 15 (2010), paper no. 62, 1930--1937. doi:10.1214/EJP.v15-826. https://projecteuclid.org/euclid.ejp/1464819847


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