Volume 17, 2013
|Page(s)||105 - 119|
|Published online||08 February 2013|
Asymptotic normality of randomly truncated stochastic algorithms
Laboratoire Jean Kuntzmann, Université de Grenoble et
CNRS, BP 53,
Grenoble Cedex 9,
Revised: 30 March 2011
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins–Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard 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 local assumptions on the expected-value function, which are fairly easy to check in practice.
Mathematics Subject Classification: 62L20 / 60F05 / 62F12
Key words: Stochastic approximation / central limit theorem / randomly truncated stochastic algorithms / martingale arrays.
© EDP Sciences, SMAI, 2013
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