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.
Keywords: stochastic approximation, central limit theorem, randomly truncated stochastic algorithms, martingale arrays
@article{PS_2013__17__105_0, 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://www.numdam.org/articles/10.1051/ps/2011110/} }
TY - JOUR AU - Lelong, Jérôme TI - Asymptotic normality of randomly truncated stochastic algorithms JO - ESAIM: Probability and Statistics PY - 2013 SP - 105 EP - 119 VL - 17 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2011110/ DO - 10.1051/ps/2011110 LA - en ID - PS_2013__17__105_0 ER -
Lelong, Jérôme. Asymptotic normality of randomly truncated stochastic algorithms. ESAIM: Probability and Statistics, Volume 17 (2013), pp. 105-119. doi : 10.1051/ps/2011110. http://www.numdam.org/articles/10.1051/ps/2011110/
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