Quasi-stationary distributions for the radial ornstein-uhlenbeck processes

The purpose of this article is to obtain the quasi-stationary distributions of the δ(δ < 2)-dimensional radial Ornstein-Uhlenbeck process with parameter -λ by using the methods of Martinez and San Martin (2001). It is described that the law of this process conditioned on first hitting 0 is just the probability measure induced by a (4-δ)-dimensional radial Ornstein-Uhlenbeck process with parameter -λ. Moreover, it is shown that the law of the conditioned process associated with the left eigenfunction of the process conditioned on first hitting 0 is induced by a one-parameter diffusion.