IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v15y1984i1p73-90.html
   My bibliography  Save this article

On the rate of convergence in the invariance principle for real-valued functions of Doeblin processes

Author

Listed:
  • Haeusler, Erich

Abstract

The speed of convergence in the functional central limit theorem (or invariance principle) for partial sum processes based on real-valued functions of Markov processes satisfying Doeblin's condition is studied where Prokhorov's metric is used to measure the distance between probability distributions on C([0, 1]). For underlying variables with finite absolute moments of an order greater than two and less than five the rate obtained is the same as that in the case of independent and identically distributed random variables which is known to be exact. The proof is based on Gordin's decomposition method and the martingale version of Skorokhod's embedding. A non-uniform Berry-Esséen estimate for the maximum absolute value of partial sums of bounded functions is also established.

Suggested Citation

  • Haeusler, Erich, 1984. "On the rate of convergence in the invariance principle for real-valued functions of Doeblin processes," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 73-90, August.
    • Handle: RePEc:eee:jmvana:v:15:y:1984:i:1:p:73-90
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(84)90068-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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:eee:jmvana:v:15:y:1984:i:1:p:73-90. 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: 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.