Uniform dimension results for a family of Markov processes

TL;DR

This paper establishes uniform Hausdorff and packing dimension results for a broad class of Markov processes, including Lévy processes and stable jump diffusions, using advanced covering principles.

Contribution

It introduces uniform dimension results for Markov process images, extending previous work with new applications to Lévy and stable-like processes.

Findings

Uniform Hausdorff and packing dimension results are proved for various Markov processes.

Applications include dimension results for Lévy processes, stable jump diffusions, and stable-like processes.

The methods rely on Xiao's covering principles.

Abstract

In this paper we prove uniform Hausdorff and packing dimension results for the images of a large family of Markov processes. The main tools are the two covering principles of Xiao (second author). As applications, uniform Hausdorff and packing dimension results for certain classes of L\'evy processes, stable jump diffusion and non-symmetric stable-like processes are obtained.