IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v379y2007i1p10-22.html
   My bibliography  Save this article

On the first passage time and leapover properties of Lévy motions

Author

Listed:
  • Koren, T.
  • Chechkin, A.V.
  • Klafter, J.

Abstract

We investigate two coupled properties of Lévy stable random motions: the first passage times (FPTs) and the first passage leapovers (FPLs). While, in general, the FPT problem has been studied quite extensively, the FPL problem has hardly attracted any attention. Considering a particle that starts at the origin and performs random jumps with independent increments chosen from a Lévy stable probability law λα,β(x), the FPT measures how long it takes the particle to arrive at or cross a target. The FPL addresses a different question: given that the first passage jump crosses the target, then how far does it get beyond the target? These two properties are investigated for three subclasses of Lévy stable motions: (i) symmetric Lévy motions characterized by Lévy index α(0<α<2) and skewness parameter β=0, (ii) one-sided Lévy motions with 0<α<1, β=1, and (iii) two-sided skewed Lévy motions, the extreme case, 1<α<2, β=−1.

Suggested Citation

  • Koren, T. & Chechkin, A.V. & Klafter, J., 2007. "On the first passage time and leapover properties of Lévy motions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 10-22.
    • Handle: RePEc:eee:phsmap:v:379:y:2007:i:1:p:10-22
    DOI: 10.1016/j.physa.2006.12.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107000349
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2006.12.039?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.

    Citations

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


    Cited by:

    1. Wijesundera, Isuri & Halgamuge, Malka N. & Nirmalathas, Ampalavanapillai & Nanayakkara, Thrishantha, 2016. "MFPT calculation for random walks in inhomogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 986-1002.
    2. Vygintas Gontis, 2021. "Order flow in the financial markets from the perspective of the Fractional L\'evy stable motion," Papers 2105.02057, arXiv.org, revised Nov 2021.
    3. Wang, Xiao & Duan, Jinqiao & Li, Xiaofan & Song, Renming, 2018. "Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 618-634.

    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:phsmap:v:379:y:2007:i:1:p:10-22. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.