IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v27y1987ip217-231.html
   My bibliography  Save this article

Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds

Author

Listed:
  • Chen, Han-Fu
  • Guo, Lei
  • Gao, Ai-Jun

Abstract

In this paper the Robbins-Monro (RM) algorithm with step-size an = 1/n and truncated at randomly varying bounds is considered under mild conditions imposed on the regression function. It is proved that for its a.s. convergence to the zero of a regression function the necessary and sufficient condition is where [xi]i denotes the measurement error. It is also shown that the algorithm is robust with respect to the measurement error in the sense that the estimation error for the sought-for zero is bounded by a function g([var epsilon]) such that

Suggested Citation

  • Chen, Han-Fu & Guo, Lei & Gao, Ai-Jun, 1987. "Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds," Stochastic Processes and their Applications, Elsevier, vol. 27, pages 217-231.
    • Handle: RePEc:eee:spapps:v:27:y:1987:i::p:217-231
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(87)90039-1
    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.

    Citations

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


    Cited by:

    1. Devang Sinha & Siddhartha P. Chakrabarty, 2022. "Multilevel Monte Carlo and its Applications in Financial Engineering," Papers 2209.14549, arXiv.org.
    2. Frikha Noufel & Sagna Abass, 2012. "Quantization based recursive importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 18(4), pages 287-326, December.
    3. Teo Sharia, 2014. "Truncated stochastic approximation with moving bounds: convergence," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 163-179, July.
    4. Devang Sinha & Siddhartha P. Chakrabarty, 2022. "Multilevel Richardson-Romberg and Importance Sampling in Derivative Pricing," Papers 2209.00821, arXiv.org.
    5. Vinayaka G. Yaji & Shalabh Bhatnagar, 2020. "Stochastic Recursive Inclusions in Two Timescales with Nonadditive Iterate-Dependent Markov Noise," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1405-1444, November.

    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:27:y:1987:i::p:217-231. 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/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.