The maximum of Brownian motion with parabolic drift (Extended abstract)
Svante Janson (1) (2), Guy Louchard (3), Anders Martin-Löf (4) (5)
(1) Department of Mathematics [Uppsala]
(2) Uppsala University
(3) Département d'Informatique [Bruxelles]
(4) Department of Mathematics Stockholm University
(5) Department of Mathematics [Stockholm]
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
[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
