Hausdorff dimension of the range and the graph of stable-like processes

2015/09/29 by Xiaochuan Yang, Yang, Xiaochuan
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1509.08759

openalex publication_date 2015/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the Hausdorff dimension for the range of a class of pure jump Markov processes in ℝ^d, which turns out to be random and depends on the trajectories of these processes. The key argument is carried out through the SDE representation of these processes. The method developed here also allows to compute the Hausdorff dimension for the graph.

Citations

• Some theorems on stable processes
• Fractal Geometry: Mathematical Foundations and Applications.
• <i>The Fractal Geometry of Nature</i>

Related

• Uniform dimension results for a family of Markov processes
• The Hausdorff dimension of the range of the Lévy multistable processes
• The dimension of the range of a transient random walk
• Hausdorff dimension in stochastic dispersion
• Multifractal analysis for the occupation measure of stable-like processes