IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v29y2016i4d10.1007_s10959-015-0626-8.html
   My bibliography  Save this article

Some Limit Theorems for Heights of Random Walks on a Spider

Author

Listed:
  • Endre Csáki

    (Hungarian Academy of Sciences)

  • Miklós Csörgő

    (Carleton University)

  • Antónia Földes

    (College of Staten Island, CUNY)

  • Pál Révész

    (Technische Universität Wien)

Abstract

A simple random walk is considered on a spider that is a collection of half lines (we call them legs) joined at the origin. We establish a strong approximation of this random walk by the so-called Brownian spider. Transition probabilities are studied, and for a fixed number of legs we investigate how high the walker and the Brownian motion can go on the legs in n steps. The heights on the legs are also investigated when the number of legs goes to infinity.

Suggested Citation

  • Endre Csáki & Miklós Csörgő & Antónia Földes & Pál Révész, 2016. "Some Limit Theorems for Heights of Random Walks on a Spider," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1685-1709, December.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:4:d:10.1007_s10959-015-0626-8
    DOI: 10.1007/s10959-015-0626-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-015-0626-8
    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/s10959-015-0626-8?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. Endre Csáki & Yueyun Hu, 2001. "Asymptotic Properties of Ranked Heights in Brownian Excursions," Journal of Theoretical Probability, Springer, vol. 14(1), pages 77-96, January.
    2. Vassilis G. Papanicolaou & Effie G. Papageorgiou & Dimitris C. Lepipas, 2012. "Random Motion on Simple Graphs," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 285-297, June.
    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. Angelos Dassios & Junyi Zhang, 2022. "First Hitting Time of Brownian Motion on Simple Graph with Skew Semiaxes," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1805-1831, September.
    2. George A. Anastassiou & Dimitra Kouloumpou, 2023. "Approximation of Brownian Motion on Simple Graphs," Mathematics, MDPI, vol. 11(20), pages 1-27, October.
    3. Endre Csáki & Yueyun Hu, 2004. "On the Ranked Excursion Heights of a Kiefer Process," Journal of Theoretical Probability, Springer, vol. 17(1), pages 145-163, January.
    4. Mohamed Abdelkader, 2023. "On the Height of One-Dimensional Random Walk," Mathematics, MDPI, vol. 11(21), pages 1-12, November.
    5. Lempa, Jukka & Mordecki, Ernesto & Salminen, Paavo, 2024. "Diffusion spiders: Green kernel, excessive functions and optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

    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:29:y:2016:i:4:d:10.1007_s10959-015-0626-8. 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.