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November 2018 Uniform dimension results for a family of Markov processes
Xiaobin Sun, Yimin Xiao, Lihu Xu, Jianliang Zhai
Bernoulli 24(4B): 3924-3951 (November 2018). DOI: 10.3150/17-BEJ994

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.

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Xiaobin Sun. Yimin Xiao. Lihu Xu. Jianliang Zhai. "Uniform dimension results for a family of Markov processes." Bernoulli 24 (4B) 3924 - 3951, November 2018. https://doi.org/10.3150/17-BEJ994

Information

Received: 1 July 2017; Revised: 1 September 2017; Published: November 2018
First available in Project Euclid: 18 April 2018

zbMATH: 06869895
MathSciNet: MR3788192
Digital Object Identifier: 10.3150/17-BEJ994

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 4B • November 2018
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