IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v27y2014i2d10.1007_s10959-012-0422-7.html
   My bibliography  Save this article

The Hausdorff Dimension of Operator Semistable Lévy Processes

Author

Listed:
  • Peter Kern

    (Heinrich-Heine-Universität Düsseldorf)

  • Lina Wedrich

    (Universität Duisburg-Essen)

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.

Suggested Citation

  • Peter Kern & Lina Wedrich, 2014. "The Hausdorff Dimension of Operator Semistable Lévy Processes," Journal of Theoretical Probability, Springer, vol. 27(2), pages 383-403, June.
    • Handle: RePEc:spr:jotpro:v:27:y:2014:i:2:d:10.1007_s10959-012-0422-7
    DOI: 10.1007/s10959-012-0422-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-012-0422-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-012-0422-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Meerschaert, Mark M. & Xiao, Yimin, 2005. "Dimension results for sample paths of operator stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 55-75, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peter Kern & Mark M. Meerschaert & Yimin Xiao, 2018. "Asymptotic Behavior of Semistable Lévy Exponents and Applications to Fractal Path Properties," Journal of Theoretical Probability, Springer, vol. 31(1), pages 598-617, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tomasz Luks & Yimin Xiao, 2017. "On the Double Points of Operator Stable Lévy Processes," Journal of Theoretical Probability, Springer, vol. 30(1), pages 297-325, March.
    2. Peter Kern & Mark M. Meerschaert & Yimin Xiao, 2018. "Asymptotic Behavior of Semistable Lévy Exponents and Applications to Fractal Path Properties," Journal of Theoretical Probability, Springer, vol. 31(1), pages 598-617, March.
    3. Cohen, Serge & Meerschaert, Mark M. & Rosinski, Jan, 2010. "Modeling and simulation with operator scaling," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2390-2411, December.
    4. Lőrinczi, József & Yang, Xiaochuan, 2019. "Multifractal properties of sample paths of ground state-transformed jump processes," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 83-94.
    5. Hou, Yanyan & Ying, Jiangang & Dai, Chaoshou, 2008. "Fractal sets determined by dilation-stable processes," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 852-863.
    6. Tomasz Luks & Yimin Xiao, 2020. "Multiple Points of Operator Semistable Lévy Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 153-179, March.
    7. R. Guével, 2019. "The Hausdorff dimension of the range of the Lévy multistable processes," Journal of Theoretical Probability, Springer, vol. 32(2), pages 765-780, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jotpro:v:27:y:2014:i:2:d:10.1007_s10959-012-0422-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.