Multiple Points of Operator Semistable Lévy Processes

Tomasz Luks () and Yimin Xiao ()
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Tomasz Luks: Universität Paderborn
Yimin Xiao: Michigan State University

Journal of Theoretical Probability, 2020, vol. 33, issue 1, 153-179

Abstract: Abstract We determine the Hausdorff dimension of the set of k-multiple points for a symmetric operator semistable Lévy process $$X=\{X(t), t\in {\mathbb {R}}_+\}$$X={X(t),t∈R+} in terms of the eigenvalues of its stability exponent. We also give a necessary and sufficient condition for the existence of k-multiple points. Our results extend to all $$k\ge 2$$k≥2 the recent work (Luks and Xiao in J Theor Probab 30(1):297–325, 2017) where the set of double points $$(k = 2)$$(k=2) was studied in the symmetric operator stable case.

Keywords: Multiple points; Hausdorff dimension; Operator semistable process; Lévy process; 60J25; 60J30; 60G51; 60G17 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-018-0859-4

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