A note on an absorption problem for a Brownian particle moving in a harmonic potential

Abstract

An analysis is presented of a Brownian particle moving on the half-line, subject to a restoring force proportional to its displacement and an absorbing boundary at the origin. When the initial displacement is large, the central moments of the time to be absorbed tend to finite constants, as do the position moments when evaluated at the most probable absorption time. These quantities are derived explicitly.