Tomasz Jakubowski

Exit Times and Poisson Kernels of the Ornstein–Uhlenbeck Diffusion

Let X t be an Ornstein–Uhlenbeck diffusion process in ℝ n and let B be an open ball in ℝ n . In this article, we study the law of τ B , the exit time of the process X t from B, the expected exit time 𝔼 x τ B , and the law of X τ B , i.e., the Poisson kernel of B. We also determine the Fourier transform of the Poisson kernel of a half-space.