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.
"The Maximum of Brownian Motion with Parabolic Drift." Electron. J. Probab. 15 1893 - 1929, 2010. https://doi.org/10.1214/EJP.v15-830