## Bernoulli

• Bernoulli
• Volume 24, Number 4B (2018), 3924-3951.

### Uniform dimension results for a family of Markov processes

#### 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 in Xiao (In Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot, Part 2 (2004) 261–338 Amer. Math. Soc.). As applications, uniform Hausdorff and packing dimension results for certain classes of Lévy processes, stable jump diffusions and non-symmetric stable-type processes are obtained.

#### Article information

Source
Bernoulli, Volume 24, Number 4B (2018), 3924-3951.

Dates
Revised: September 2017
First available in Project Euclid: 18 April 2018

https://projecteuclid.org/euclid.bj/1524038773

Digital Object Identifier
doi:10.3150/17-BEJ994

Mathematical Reviews number (MathSciNet)
MR3788192

Zentralblatt MATH identifier
06869895

#### Citation

Sun, Xiaobin; Xiao, Yimin; Xu, Lihu; Zhai, Jianliang. Uniform dimension results for a family of Markov processes. Bernoulli 24 (2018), no. 4B, 3924--3951. doi:10.3150/17-BEJ994. https://projecteuclid.org/euclid.bj/1524038773

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