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2010 The Maximum of Brownian Motion with Parabolic Drift
Svante Janson, Guy Louchard, Anders Martin-Löf
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Electron. J. Probab. 15: 1893-1929 (2010). DOI: 10.1214/EJP.v15-830


We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give new series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.


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Svante Janson. Guy Louchard. Anders Martin-Löf. "The Maximum of Brownian Motion with Parabolic Drift." Electron. J. Probab. 15 1893 - 1929, 2010.


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

zbMATH: 1226.60111
MathSciNet: MR2738342
Digital Object Identifier: 10.1214/EJP.v15-830

Primary: 60J65

Keywords: Airy functions , Brownian motion , parabolic drift

Vol.15 • 2010
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