The Hausdorff Dimension of Operator Semistable Lévy Processes

Peter Kern () and Lina Wedrich ()
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Peter Kern: Heinrich-Heine-Universität Düsseldorf
Lina Wedrich: Universität Duisburg-Essen

Journal of Theoretical Probability, 2014, vol. 27, issue 2, 383-403

Abstract: Abstract Let X={X(t)} t≥0 be an operator semistable Lévy process in ℝ d with exponent E, where E is an invertible linear operator on ℝ d 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.

Keywords: Lévy process; Operator semistable process; Semi-selfsimilarity; Sojourn time; Range; Hausdorff dimension; Positivity of density; 60G51; 28A78; 28A80; 60G17; 60G52 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-012-0422-7

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