Harnack Inequalities for Ornstein-Uhlenbeck Processes Driven by Lévy Processes

Abstract

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

11 pages

References in corpus (3)

• Harnack inequality and applications for stochastic generalized porous media equations
• Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
• Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump