Harnack Inequalities for Ornstein-Uhlenbeck Processes Driven by Lévy Processes

Details Harnack Inequalities for Ornstein-Uhlenbeck Processes Driven by Lévy Processes Harnack Inequalities for Ornstein-Uhlenbeck Processes Driven by Lévy Processes

2011-05-15

arxiv.org/abs/1105.2958v1

Mathematics

Probability

11 pages

Scientific paper

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

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