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.