Volume 17, 2013
|Page(s)||179 - 194|
|Published online||08 February 2013|
On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms
Institut de Mathématiques de Bourgogne, IMB UMR 5584
CNRS, 9 rue Alain
Received: 1 October 2010
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.
Mathematics Subject Classification: 60F05 / 62L20 / 60G42
Key words: Stochastic approximation algorithms / almost sure central limit theorem / martingale transforms / moments
© EDP Sciences, SMAI, 2013
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