Uniform dimension results for the inverse images of symmetric Lévy processes

Abstract

We prove uniform Hausdorff and packing dimension results for the inverse images of a large class of real-valued symmetric Lévy processes. Our main result for the Hausdorff dimension extends that of Kaufman (1985) for Brownian motion and that of Song, Xiao, and Yang (2018) for $\alpha$-stable Lévy processes with $1<\alpha <2$. Along the way, we also prove an upper bound for the uniform modulus of continuity of the local times of these processes.

19 pages, to appear in JOTP