The Maximum of Brownian Motion Minus a Parabola

Piet Groeneboom

doi:10.1214/EJP.v15-826

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Home > Journals > Electron. J. Probab. > Volume 15 > Article

2010 The Maximum of Brownian Motion Minus a Parabola

Piet Groeneboom

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Piet Groeneboom¹
¹Delft University of Technology

Electron. J. Probab. 15: 1930-1937 (2010). DOI: 10.1214/EJP.v15-826

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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.

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Piet Groeneboom. "The Maximum of Brownian Motion Minus a Parabola." Electron. J. Probab. 15 1930 - 1937, 2010. https://doi.org/10.1214/EJP.v15-826

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Accepted: 17 November 2010; Published: 2010

First available in Project Euclid: 1 June 2016

zbMATH: 1226.60110

MathSciNet: MR2738343

Digital Object Identifier: 10.1214/EJP.v15-826

Subjects:

Primary: 60J65

Secondary: 60J75

Keywords: Airy functions , Brownian motion , Maximum , parabolic drift

Rights: Creative Commons Attribution 3.0 License

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Piet Groeneboom "The Maximum of Brownian Motion Minus a Parabola," Electronic Journal of Probability, Electron. J. Probab. 15(none), 1930-1937, (2010)

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