IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v129y2019i11p4663-4686.html
   My bibliography  Save this article

On the centre of mass of a random walk

Author

Listed:
  • Lo, Chak Hei
  • Wade, Andrew R.

Abstract

For a random walk Sn on Rd we study the asymptotic behaviour of the associated centre of mass process Gn=n−1∑i=1nSi. For lattice distributions we give conditions for a local limit theorem to hold. We prove that if the increments of the walk have zero mean and finite second moment, Gn is recurrent if d=1 and transient if d≥2. In the transient case we show that Gn has a diffusive rate of escape. These results extend work of Grill, who considered simple symmetric random walk. We also give a class of random walks with symmetric heavy-tailed increments for which Gn is transient in d=1.

Suggested Citation

  • Lo, Chak Hei & Wade, Andrew R., 2019. "On the centre of mass of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4663-4686.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:11:p:4663-4686
    DOI: 10.1016/j.spa.2018.12.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918307130
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2018.12.007?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. Grill, Karl, 1988. "On the average of a random walk," Statistics & Probability Letters, Elsevier, vol. 6(5), pages 357-361, April.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Bercu, Bernard & Laulin, Lucile, 2021. "On the center of mass of the elephant random walk," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 111-128.

    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. Bercu, Bernard & Laulin, Lucile, 2021. "On the center of mass of the elephant random walk," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 111-128.
    2. Hryniv, Ostap & Menshikov, Mikhail V. & Wade, Andrew R., 2013. "Excursions and path functionals for stochastic processes with asymptotically zero drifts," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1891-1921.

    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:11:p:4663-4686. 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.