Harnack inequalities for Ornstein–Uhlenbeck processes driven by Lévy processes

By using the existing sharp estimates of the density function for rotationally invariant symmetric αα-stable Lévy processes and rotationally invariant symmetric truncated αα-stable Lévy processes, we obtain that the Harnack inequalities hold for rotationally invariant symmetric αα-stable Lévy processes with α∈(0,2)α∈(0,2) and Ornstein–Uhlenbeck processes driven by rotationally invariant symmetric αα-stable Lévy process, while the logarithmic Harnack inequalities are satisfied for rotationally invariant symmetric truncated αα-stable Lévy processes.