  We revise the classical problem of characterizing first exit times of a
harmonically trapped particle whose motion is described by one- or
multi-dimensional Ornstein-Uhlenbeck process. We start by recalling the main
derivation steps of a propagator using Langevin and Fokker-Planck equations.
The mean exit time, the moment-generating function, and the survival
probability are then expressed through confluent hypergeometric functions and
thoroughly analyzed. We also present a rapidly converging series representation
of confluent hypergeometric functions that is particularly well suited for
numerical computation of eigenvalues and eigenfunctions of the governing
Fokker-Planck operator. We discuss several applications of first exit times
such as detection of time intervals during which motor proteins exert a
constant force onto a tracer in optical tweezers single-particle tracking
experiments; adhesion bond dissociation under mechanical stress;
characterization of active periods of trend following and mean-reverting
strategies in algorithmic trading on stock markets; relation to the
distribution of first crossing times of a moving boundary by Brownian motion.
Some extensions are described, including diffusion under quadratic double-well
potential and anomalous diffusion.
