The one-sided barrier problem for an integrated ornstein-uhlenbeck process

Abstract

The first-passage problem is considered for the process where V(s) is an Ornstein-Uhlenbeck process with an additive constant term μ friction parameter β, and variance σ2 starting from V(O)=μ+μ Global explicit analytic approximations to the first-passage density are derived for the case of a one-sided fixed barrier at distance x from X (0). By a series of simulations the quality of these approximations is studied for varies χ,ν,β,μ,σ2. We also consider an application to stochastic models for particle sedimentation in fluids where the first-passage problem of an integrated Ornstein-Uhlenbeck process naturally arises.