Multiple Points of Operator Semistable Lévy Processes

  • Tomasz LuksEmail author
  • Yimin Xiao


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.


Multiple points Hausdorff dimension Operator semistable process Lévy process 

Mathematics Subject Classification (2010)

60J25 60J30 60G51 60G17 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für MathematikUniversität PaderbornPaderbornGermany
  2. 2.Department of Statistics and ProbabilityMichigan State UniversityEast LansingUSA

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