The estimates of the mean first exit time from a ball for the [alpha]-stable Ornstein-Uhlenbeck processes

We consider the [alpha]-stable Ornstein-Uhlenbeck process as a solution of the Langevin equation where the Brownian motion is replaced by an isotropic [alpha]-stable process. We give sharp estimates for the expectation of the first exit time from the center of a ball B(x,r) for all and r>0. We compare these results with the case of the Ornstein-Uhlenbeck diffusion process.