A similarity solution for the Ornstein-Uhlenbeck diffusion process constrained by a reflecting and an absorbing boundary

One-parameter Lie groups of transformations are employed to obtain the transition probability density function for an Ornstein-Uhlenbeck time homogeneous diffusion process constrained by a lower reflecting and an upper absorbing boundary. The solution is expressed as a series of confluent hypergeometric functions. The interest in determining the solution of such problem by means of similarity methods is confirmed by the extended use of the constrained Ornstien-Uhlenbeck process in various fields of application.