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Multiple Points of Operator Semistable Lévy Processes

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Abstract

We determine the Hausdorff dimension of the set of k-multiple points for a symmetric operator semistable Lévy process \(X=\{X(t), t\in {\mathbb {R}}_+\}\) 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 \(k\ge 2\) the recent work (Luks and Xiao in J Theor Probab 30(1):297–325, 2017) where the set of double points \((k = 2)\) was studied in the symmetric operator stable case.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Paderborn, Warburger Strasse 100, 33098, Paderborn, Germany

    Tomasz Luks

  2. Department of Statistics and Probability, Michigan State University, 619 Red Cedar Road, C413 Wells Hall, East Lansing, MI, 48824-1027, USA

    Yimin Xiao

Authors
  1. Tomasz Luks
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  2. Yimin Xiao
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Correspondence to Tomasz Luks.

Additional information

Research of Y. Xiao was partially supported by the NSF Grants DMS-1612885 and DMS-1607089.

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Luks, T., Xiao, Y. Multiple Points of Operator Semistable Lévy Processes. J Theor Probab 33, 153–179 (2020). https://doi.org/10.1007/s10959-018-0859-4

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  • DOI: https://doi.org/10.1007/s10959-018-0859-4

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