Hausdorff Dimension of the Range and the Graph of Stable-Like Processes

Xiaochuan Yang ()
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Xiaochuan Yang: Michigan State University

Journal of Theoretical Probability, 2018, vol. 31, issue 4, 2412-2431

Abstract: Abstract We determine the Hausdorff dimension for the range of a class of pure jump Markov processes in $$\mathbb {R}^d$$ R d , which turns out to be random and depends on the trajectories of these processes. The key argument is carried out through the SDE representation of these processes. The method developed here also allows to compute the Hausdorff dimension for the graph.

Keywords: Markov processes; Lévy processes; Hausdorff dimension; 60H10; 60J25; 60J75; 28A78 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-017-0784-y

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