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Asymptotic normality of randomly truncated stochasticalgorithms

Published online by Cambridge University Press:  08 February 2013

Jérôme Lelong
Jérôme Lelong*
Affiliation:
Laboratoire Jean Kuntzmann, Université de Grenoble et CNRS, BP 53, 38041 Grenoble Cedex 9, France. jerome.lelong@imag.fr
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Abstract

We study the convergence rate of randomly truncated stochastic algorithms, which consistin the truncation of the standard Robbins–Monro procedure on an increasing sequence ofcompact sets. Such a truncation is often required in practice to ensure convergence whenstandard algorithms fail because the expected-value function grows too fast. In this work,we give a self contained proof of a central limit theorem for this algorithm under localassumptions on the expected-value function, which are fairly easy to check in practice.

Keywords

Stochastic approximationcentral limit theoremrandomly truncated stochastic algorithmsmartingale arrays.

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 105 - 119
Copyright
© EDP Sciences, SMAI, 2013

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