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Asymptotic normality of randomly truncated stochastic algorithms
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 105-119

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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.

DOI : 10.1051/ps/2011110
Classification : 62L20, 60F05, 62F12
Keywords: stochastic approximation, central limit theorem, randomly truncated stochastic algorithms, martingale arrays 
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     author = {Lelong, J\'er\^ome},
     title = {Asymptotic normality of randomly truncated stochastic algorithms},
     journal = {ESAIM: Probability and Statistics},
     pages = {105--119},
     publisher = {EDP-Sciences},
     volume = {17},
     year = {2013},
     doi = {10.1051/ps/2011110},
     mrnumber = {3021311},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2011110/}
}
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Lelong, Jérôme. Asymptotic normality of randomly truncated stochastic algorithms. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 105-119. doi: 10.1051/ps/2011110

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