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The Hausdorff Dimension of Operator Semistable Lévy Processes

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Abstract

Let X={X(t)} t≥0 be an operator semistable Lévy process in ℝd with exponent E, where E is an invertible linear operator on ℝd and X is semi-selfsimilar with respect to E. By refining arguments given in Meerschaert and Xiao (Stoch. Process. Appl. 115, 55–75, 2005) for the special case of an operator stable (selfsimilar) Lévy process, for an arbitrary Borel set B⊆ℝ+ we determine the Hausdorff dimension of the partial range X(B) in terms of the real parts of the eigenvalues of E and the Hausdorff dimension of B.

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Authors and Affiliations

  1. Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany

    Peter Kern

  2. Fakultät für Wirtschaftswissenschaften, Universität Duisburg-Essen, Campus Essen, Universitätsstr. 12, 45141, Essen, Germany

    Lina Wedrich

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  1. Peter Kern
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  2. Lina Wedrich
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Correspondence to Peter Kern.

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Kern, P., Wedrich, L. The Hausdorff Dimension of Operator Semistable Lévy Processes. J Theor Probab 27, 383–403 (2014). https://doi.org/10.1007/s10959-012-0422-7

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  • DOI: https://doi.org/10.1007/s10959-012-0422-7

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