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arXiv · 1903.10009

Uniform dimension results for the inverse images of symmetric L\'evy processes

Hyunchul Park·Yimin Xiao·Xiaochuan Yang
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Abstract

We prove uniform Hausdorff and packing dimension results for the inverse images of a large class of real-valued symmetric L\'evy 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 L\'evy 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.

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Hyunchul Park, Yimin Xiao, Xiaochuan Yang. 2019-03-24. Uniform dimension results for the inverse images of symmetric L\'evy processes. https://arxiv.org/abs/1903.10009

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