Vertices of the Least Concave Majorant of Brownian Motion with Parabolic Drift

The Concave Majorant of Brownian Motion

The maximum of Brownian motion with parabolic drift ( Extended 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 n...

The Maximum of Brownian Motion with Parabolic Drift

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.

Moments of the location of the maximum of Brownian motion with parabolic drift∗

We derive integral formulas, involving the Airy function, for moments of the time a two-sided Brownian motion with parabolic drift attains its maximum.

Brownian Motion with Polar Drift

Consider a strong Markov process X° that has continuous sample paths in Rd (d > 2) and the following two properties. (1) Away from the origin X° behaves like Brownian motion with a polar drift given in spherical polar coordinates by n{8)/2r. Here /i is a bounded Borel measurable function on the unit sphere in RJ, with average value Ji. (2) X° is absorbed at the origin. It is shown that X° reach...