On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 179-194.

We study the almost sure asymptotic behaviour of stochastic approximation algorithms for the search of zero of a real function. The quadratic strong law of large numbers is extended to the powers greater than one. In other words, the convergence of moments in the almost sure central limit theorem (ASCLT) is established. As a by-product of this convergence, one gets another proof of ASCLT for stochastic approximation algorithms. The convergence result is applied to several examples as estimation of quantiles and recursive estimation of the mean.

DOI : 10.1051/ps/2011155
Classification : 60F05, 62L20, 60G42
Mots clés : stochastic approximation algorithms, almost sure central limit theorem, martingale transforms, moments
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     author = {C\'enac, Peggy},
     title = {On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms},
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     pages = {179--194},
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     url = {http://archive.numdam.org/articles/10.1051/ps/2011155/}
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Cénac, Peggy. On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 179-194. doi : 10.1051/ps/2011155. http://archive.numdam.org/articles/10.1051/ps/2011155/

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