Electronic Journal of Probability

The Maximum of Brownian Motion with Parabolic Drift

Svante Janson, Guy Louchard, and Anders Martin-Löf

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 61, 1893-1929.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819846

Digital Object Identifier
doi:10.1214/EJP.v15-830

Mathematical Reviews number (MathSciNet)
MR2738342

Zentralblatt MATH identifier
1226.60111

Subjects
Primary: 60J65: Brownian motion [See also 58J65]

Keywords
Brownian motion parabolic drift Airy functions

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

Citation

Janson, Svante; Louchard, Guy; Martin-Löf, Anders. The Maximum of Brownian Motion with Parabolic Drift. Electron. J. Probab. 15 (2010), paper no. 61, 1893--1929. doi:10.1214/EJP.v15-830. https://projecteuclid.org/euclid.ejp/1464819846


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