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

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.
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Svante Janson, Guy Louchard, Anders Martin-Löf. The maximum of Brownian motion with parabolic drift (Extended abstract). 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. pp.427-438, ⟨10.46298/dmtcs.2766⟩. ⟨hal-01185564⟩

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