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

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