First passage times for Slepian process with linear and piecewise linear barriers

Abstract In this paper, we derive explicit formulas for the first-passage probabilities of process S ( t ) = W − + 1), where is Brownian motion, linear and piece-wise barriers on arbitrary intervals [0, T ]. Previously, were known only cases a constant barrier or ≤ 1. The results are used to power familiar test change-point detection in Wiener process.