Rigorous results for mean first-passage time of harmonically trapped particle

The Ornstein-Uhlenbeck process of diffusion in the harmonic potential is re-examined in the context of the first-passage time problem. We investigate this problem to the extent that it has not yet been fully resolved and demonstrate exact novel results. They mainly concern the mean first-passage time for a particle diffusing downward and upward in the harmonic potential. We verify the main results of this paper by using a number of analytical techniques.