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


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


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

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    Cited by:

    1. Teo Sharia, 2014. "Truncated stochastic approximation with moving bounds: convergence," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 163-179, July.
    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.


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