Advanced Search
MyIDEAS: Login

Martingales and the Robbins-Monro procedure in D[0, 1]


Author Info

  • Walk, H.
Registered author(s):


    The Robbins-Monro procedure for recursive estimation of a zero point of a regression function f is investigated for the case f defined on and with values in the space D[0, 1] of real-valued functions on [0, 1] that are right-continuous and have left-hand limits, endowed with Skorohod's J1-topology. There are proved an a.s. convergence result and an invariance principle where the limit process is a Gaussian Markov process with paths in the space of continuous C[0, 1]-valued functions on [0, 1]. At first the case f(x) [reverse not equivalent] x, i.e., the case of a martingale in D[0, 1], is treated and by this then the general case. An application to an initial value problem with only empirically available function values is sketched.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 8 (1978)
    Issue (Month): 3 (September)
    Pages: 430-452

    as in new window
    Handle: RePEc:eee:jmvana:v:8:y:1978:i:3:p:430-452

    Contact details of provider:
    Web page:

    Order Information:

    Related research

    Keywords: Robbins-Monro process in D[0; 1] martingales in D[0; 1] strong theorems invariance principles Gaussian process Brownian motion in C[0; 1] initial value problem;


    No references listed on IDEAS
    You can help add them by filling out this form.


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

    Cited by:
    1. Soonhui Lee & Tito Homem-de-Mello & Anton Kleywegt, 2012. "Newsvendor-type models with decision-dependent uncertainty," Computational Statistics, Springer, vol. 76(2), pages 189-221, October.


    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:8:y:1978:i:3:p:430-452. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.