A note on the moments of the first-passage-time of the Ornstein-Uhlenbeck process with a reflecting boundary

For the Ornstein-Uhlenbeck process with a reflecting boundary the moments of the first-passage time through a constant boundary are obtained in a closed form that appears to be particularly suitable for computation purposes. This is achieved via the determination of the Laplace transform of the first-passage time probability density function by a method previously devised by L. M. Ricciardi and S. Sato [J. Appl. Probab. 25, No. 1, 43–57 (1988; Zbl 651.60080)] for the unrestricted case.