IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v18y2012i2p181-200n5.html
   My bibliography  Save this article

Probabilistic error bounds for the discrepancy of mixed sequences

Author

Listed:
  • Aistleitner Christoph

    (Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria)

  • Hofer Markus

    (Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria)

Abstract

In many applications Monte Carlo (MC) sequences or Quasi-Monte Carlo (QMC) sequences are used for numerical integration. In moderate dimensions the QMC method typically yield better results, but its performance significantly falls off in quality if the dimension increases. One class of randomized QMC sequences, which try to combine the advantages of MC and QMC, are so-called mixed sequences, which are constructed by concatenating a d-dimensional QMC sequence and an ()-dimensional MC sequence to obtain a sequence in dimension s. Ökten, Tuffin and Burago proved probabilistic asymptotic bounds for the discrepancy of mixed sequences, which were refined by Gnewuch. In this paper we use an interval partitioning technique to obtain improved probabilistic bounds for the discrepancy of mixed sequences. By comparing them with lower bounds we show that our results are almost optimal.

Suggested Citation

  • Aistleitner Christoph & Hofer Markus, 2012. "Probabilistic error bounds for the discrepancy of mixed sequences," Monte Carlo Methods and Applications, De Gruyter, vol. 18(2), pages 181-200, January.
    • Handle: RePEc:bpj:mcmeap:v:18:y:2012:i:2:p:181-200:n:5
    DOI: 10.1515/mcma-2012-0006
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mcma-2012-0006
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/mcma-2012-0006?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.

    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:bpj:mcmeap:v:18:y:2012:i:2:p:181-200:n:5. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.