IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v107y2015icp264-271.html
   My bibliography  Save this article

On the almost sure invariance principle for dependent Bernoulli random variables

Author

Listed:
  • Zhang, Yang
  • Zhang, Li-Xin

Abstract

We consider a sequence of dependent Bernoulli variables where the success probability of the trial conditional on the past history is a linear function of the mean number of successes achieved to that point. An almost sure invariance principle is established for the partial sum and we also generalize the model to a multi-dimensional case, extending the results of Heyde (2004), James et al. (2008) and Wu et al. (2012).

Suggested Citation

  • Zhang, Yang & Zhang, Li-Xin, 2015. "On the almost sure invariance principle for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 264-271.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:264-271
    DOI: 10.1016/j.spl.2015.09.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215003272
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.09.008?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. repec:bla:anzsta:v:46:y:2004:i:1:p:53-57 is not listed on IDEAS
    2. James, Barry & James, Kang & Qi, Yongcheng, 2008. "Limit theorems for correlated Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2339-2345, October.
    3. Wu, Lan & Qi, Yongcheng & Yang, Jingping, 2012. "Asymptotics for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 455-463.
    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. Gava, Renato J. & Rezende, Bruna L.F., 2021. "Some limit theorems for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 170(C).

    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. Gava, Renato J. & Rezende, Bruna L.F., 2021. "Some limit theorems for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 170(C).
    2. Zhang, Li-Xin & Zhang, Yang, 2015. "Asymptotics for a class of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 47-56.
    3. Alessandro Arlotto & Noah Gans & J. Michael Steele, 2014. "Markov Decision Problems Where Means Bound Variances," Operations Research, INFORMS, vol. 62(4), pages 864-875, August.
    4. Gut, Allan & Stadtmüller, Ulrich, 2022. "The elephant random walk with gradually increasing memory," Statistics & Probability Letters, Elsevier, vol. 189(C).
    5. Modarres, Reza, 2011. "High-dimensional generation of Bernoulli random vectors," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1136-1142, August.
    6. Wu, Lan & Qi, Yongcheng & Yang, Jingping, 2012. "Asymptotics for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 455-463.
    7. Peter Farkas & Laszlo Matyas, 2015. "Testing for Unit Roots in Panel Data with Boundary Crossing Counts," CEU Working Papers 2015_5, Department of Economics, Central European University, revised 03 Nov 2015.

    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:stapro:v:107:y:2015:i:c:p:264-271. 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/622892/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.