IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v120y2019icp83-94.html
   My bibliography  Save this article

Multifractal properties of sample paths of ground state-transformed jump processes

Author

Listed:
  • Lőrinczi, József
  • Yang, Xiaochuan

Abstract

We consider a class of Lévy-type processes with unbounded coefficients, arising as Doob h-transforms of Feynman-Kac type representations of non-local Schrödinger operators, where the function h is chosen to be the ground state of such an operator. First we show existence of a càdlàg version of the so-obtained ground state-transformed processes. Next we prove that they satisfy a related stochastic differential equation with jumps. Making use of this SDE, we then derive and prove the multifractal spectrum of local Hölder exponents of sample paths of ground state-transformed processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:83-94
    DOI: 10.1016/j.chaos.2019.01.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919300141
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.01.008?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.
    2. Xu, Liping, 2016. "The multifractal nature of Boltzmann processes," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2181-2210.
    3. Kaleta, Kamil & Lőrinczi, József, 2012. "Fractional P(ϕ)1-processes and Gibbs measures," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3580-3617.
    Full references (including those not matched with items on IDEAS)

    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. Tomasz Luks & Yimin Xiao, 2020. "Multiple Points of Operator Semistable Lévy Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 153-179, March.
    4. 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.
    5. 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.
    6. 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.
    7. Hou, Yanyan & Ying, Jiangang & Dai, Chaoshou, 2008. "Fractal sets determined by dilation-stable processes," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 852-863.

    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:chsofr:v:120:y:2019:i:c:p:83-94. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.