The maximum of Brownian motion with parabolic drift (Extended abstract)

Svante Janson 1, 2 Guy Louchard 3 Anders Martin-Löf 4
1 Department of Mathematics [Uppsala]
2 Uppsala University
3 ULB - Département d'Informatique [Bruxelles]
4 Department of Mathematics Stockholm University
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. This has some applications in algorithmic and data structures analysis. We give series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.
Keywords : Brownian motion parabolic drift Airy functions.
Type de document :
Communication dans un congrès
Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.427-438, 2010, DMTCS Proceedings
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Svante Janson, Guy Louchard, Anders Martin-Löf. The maximum of Brownian motion with parabolic drift (Extended abstract). Drmota, Michael and Gittenberger, Bernhard. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp.427-438, 2010, DMTCS Proceedings. 〈hal-01185564〉

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