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

2018/01/09 by Renming Song, Song, Renming, Yimin Xiao +3
Economics, Econometrics and Finance · Mathematics · #28A80 #60G17 #60G52 #60J75 #FOS: Mathematics #Fuzzy Systems and Optimization #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1801.03008

openalex publication_date 2018/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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