First-passage theory for Brownian motion with an absorbing boundary

Abstract

Considers the problem of Brownian motion (1-D) with an absorbing barrier. The approach is the first-passage-time theory recently formulated by us. Explicit results for the position velocity distribution function are obtained in a high-friction approximation which indicate the usefulness of this approach in determining approximate solutions. An improved approximation, which retains the initial velocity dependence, is then considered, and results obtained which contain much of the qualitative behaviour one would expect to find in the exact solution. Some consequences of the initial velocity dependence in a calculation of the number density are briefly examined.