IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v129y2019i12p5151-5199.html
   My bibliography  Save this article

Asymptotically stable random walks of index 1<α<2 killed on a finite set

Author

Listed:
  • Uchiyama, Kôhei

Abstract

For a random walk on the integer lattice Z that is attracted to a strictly stable process with index α∈(1,2) we obtain the asymptotic form of the transition probability for the walk killed when it hits a finite set. The asymptotic forms obtained are valid uniformly in a natural range of the space and time variables. The situation is relatively simple when the limit stable process has jumps in both positive and negative directions; in the other case when the jumps are one sided rather interesting matters are involved and detailed analyses are necessitated.

Suggested Citation

  • Uchiyama, Kôhei, 2019. "Asymptotically stable random walks of index 1<α<2 killed on a finite set," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5151-5199.
  • Handle: RePEc:eee:spapps:v:129:y:2019:i:12:p:5151-5199
    DOI: 10.1016/j.spa.2019.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918301613
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2019.02.006?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. Vysotsky, Vladislav, 2015. "Limit theorems for random walks that avoid bounded sets, with applications to the largest gap problem," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1886-1910.
    2. Uchiyama, Kôhei, 2017. "One dimensional random walks killed on a finite set," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2864-2899.
    3. Uchiyama, Kôhei, 2011. "A note on summability of ladder heights and the distributions of ladder epochs for random walks," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 1938-1961, September.
    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. Kôhei Uchiyama, 2020. "Scaling Limits of Random Walk Bridges Conditioned to Avoid a Finite Set," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1296-1326, September.
    2. Gerold Alsmeyer & Alexander Iksanov & Matthias Meiners, 2015. "Power and Exponential Moments of the Number of Visits and Related Quantities for Perturbed Random Walks," Journal of Theoretical Probability, Springer, vol. 28(1), pages 1-40, March.
    3. Micha Buck, 2021. "Limit Theorems for Random Walks with Absorption," Journal of Theoretical Probability, Springer, vol. 34(1), pages 241-263, March.
    4. Döring, Leif & Kyprianou, Andreas E. & Weissmann, Philip, 2020. "Stable processes conditioned to avoid an interval," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 471-487.

    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:129:y:2019:i:12:p:5151-5199. 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.