IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v23y2010i4d10.1007_s10959-009-0244-4.html
   My bibliography  Save this article

Weak Convergence Theorem of a Nonnegative Random Walk to Sticky Reflected Brownian Motion

Author

Listed:
  • Hirotaka Fushiya

    (Aoyama Gakuin University)

Abstract

We obtain a convergence theorem of a 1-dimensional sticky reflected random walk with state space R +. It behaves like a random walk if it is away from the origin. Once it reaches 0, it stays at 0 for a while and is then repelled to the positive region. We consider its tightness and a martingale problem for a discontinuous function in order to construct a weak convergence theorem.

Suggested Citation

  • Hirotaka Fushiya, 2010. "Weak Convergence Theorem of a Nonnegative Random Walk to Sticky Reflected Brownian Motion," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1157-1181, December.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:4:d:10.1007_s10959-009-0244-4
    DOI: 10.1007/s10959-009-0244-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-009-0244-4
    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/s10959-009-0244-4?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. Amir, Madjid, 1991. "Sticky Brownian motion as the strong limit of a sequence of random walks," Stochastic Processes and their Applications, Elsevier, vol. 39(2), pages 221-237, December.
    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. Alexis Anagnostakis, 2023. "Pricing and hedging for a sticky diffusion," Papers 2311.17011, arXiv.org, revised Jan 2024.
    2. Hongshuai Dai, 2022. "Tandem fluid queue with long-range dependent inputs: sticky behaviour and heavy traffic approximation," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 165-196, June.
    3. Amir, Madjid & Knight, Frank B., 1995. "Law of the iterated logarithm and local variations at zero of the sticky Brownian motion," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 289-295, May.
    4. Christian Meier & Lingfei Li & Gongqiu Zhang, 2019. "Markov Chain Approximation of One-Dimensional Sticky Diffusions," Papers 1910.14282, arXiv.org.

    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:23:y:2010:i:4:d:10.1007_s10959-009-0244-4. 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.