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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
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    Cited by:

    1. Devang Sinha & Siddhartha P. Chakrabarty, 2022. "Multilevel Monte Carlo and its Applications in Financial Engineering," Papers 2209.14549, arXiv.org.
    2. Teo Sharia, 2014. "Truncated stochastic approximation with moving bounds: convergence," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 163-179, July.
    3. Devang Sinha & Siddhartha P. Chakrabarty, 2022. "Multilevel Richardson-Romberg and Importance Sampling in Derivative Pricing," Papers 2209.00821, arXiv.org.
    4. Frikha Noufel & Sagna Abass, 2012. "Quantization based recursive importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 18(4), pages 287-326, December.
    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.

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