Uniform dimension results for a family of Markov processes

Xiaobin Sun; Yimin Xiao; Lihu Xu; Jianliang Zhai

Uniform dimension results for a family of Markov processes

Probability 2017-10-03 v2

Authors: Xiaobin Sun , Yimin Xiao , Lihu Xu , Jianliang Zhai

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.

Keywords

markov processes hausdorff dimension packing dimension uniform dimension results covering principles l\'evy processes stable jump diffusion

Cite

@article{arxiv.1707.03102,
  title  = {Uniform dimension results for a family of Markov processes},
  author = {Xiaobin Sun and Yimin Xiao and Lihu Xu and Jianliang Zhai},
  journal= {arXiv preprint arXiv:1707.03102},
  year   = {2017}
}

Comments

We revised the assumptions (A2) and (A3) in the previous version, the new assumptions are more general and expected to cover more examples

Uniform dimension results for a family of Markov processes

Abstract

Keywords

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