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

We consider the α -stable Ornstein–Uhlenbeck process as a solution of the Langevin equation where the Brownian motion is replaced by an isotropic α -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 x ∈ R d and r > 0 . We compare these results with the case of the Ornstein–Uhlenbeck diffusion process.