IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v115y2005i1p55-75.html
   My bibliography  Save this article

Dimension results for sample paths of operator stable Lévy processes

Author

Listed:
  • Meerschaert, Mark M.
  • Xiao, Yimin

Abstract

Let X= X(t),t[set membership, variant]R+ be an operator stable Lévy process in Rd with exponent B, where B is an invertible linear operator on Rd. We determine the Hausdorff dimension and the packing dimension of the range X([0,1]) in terms of the real parts of the eigenvalues of B.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:115:y:2005:i:1:p:55-75
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(04)00132-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Xiao, Yimin, 1997. "Packing dimension of the image of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 379-387, May.
    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. Tomasz Luks & Yimin Xiao, 2020. "Multiple Points of Operator Semistable Lévy Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 153-179, March.
    2. 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.
    3. 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.
    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. 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.
    7. 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.
    8. 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. Xiao, Yimin, 2009. "A packing dimension theorem for Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 88-97, January.
    2. Li, Jinjun, 2011. "A class of probability distribution functions preserving the packing dimension," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1782-1791.
    3. Falconer, Kenneth J., 2022. "Intermediate dimension of images of sequences under fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 182(C).
    4. Stuart A. Burrell, 2022. "Dimensions of Fractional Brownian Images," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2217-2238, December.
    5. Daw, Lara & Kerchev, George, 2023. "Fractal dimensions of the Rosenblatt process," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 544-571.
    6. Lou, Shuwen & Ouyang, Cheng, 2016. "Fractal dimensions of rough differential equations driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2410-2429.
    7. Du, Yali & Miao, Junjie & Wu, Dongsheng & Xiao, Yimin, 2015. "Packing dimensions of the images of Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 209-217.

    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:eee:spapps:v:115:y:2005:i:1:p:55-75. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.