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On the Double Points of Operator Stable Lévy Processes

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Abstract

We determine the Hausdorff dimension of the set of double points for a symmetric operator stable Lévy process \(X=\left\{ X(t),t\in \mathbb {R}_+\right\} \) in terms of the eigenvalues of its stability exponent.

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Authors and Affiliations

  1. Institut de Mathématiques de Marseille, Ecole Centrale de Marseille, I2M, 38 Rue Frédéric Joliot Curie, 13013, Marseille, France

    Tomasz Luks

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

    Tomasz Luks & Yimin Xiao

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

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Disclosure of potential conflicts of interest

Research of T. Luks was partially supported by Agence Nationale de la Recherche Grant ANR-09-BLAN-0084-01. Research of Y. Xiao was partially supported by the NSF Grants DMS-1307470 and DMS-1309856.

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Luks, T., Xiao, Y. On the Double Points of Operator Stable Lévy Processes. J Theor Probab 30, 297–325 (2017). https://doi.org/10.1007/s10959-015-0638-4

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  • DOI: https://doi.org/10.1007/s10959-015-0638-4

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