Uniform Hausdorff dimension result for the inverse images of stable Lévy processes

Abstract

We establish a uniform Hausdorff dimension result for the inverse image sets of real-valued strictly $\alpha $-stable Lévy processes with $1< \alpha \le 2$. This extends a theorem of Kaufman [11] for Brownian motion. Our method is different from that of [11] and depends on covering principles for Markov processes.