# On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms

ESAIM: Probability and Statistics (2013)

- Volume: 17, page 179-194
- ISSN: 1292-8100

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topCénac, Peggy. "On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms." ESAIM: Probability and Statistics 17 (2013): 179-194. <http://eudml.org/doc/273615>.

@article{Cénac2013,

abstract = {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.},

author = {Cénac, Peggy},

journal = {ESAIM: Probability and Statistics},

keywords = {stochastic approximation algorithms; almost sure central limit theorem; martingale transforms; moments},

language = {eng},

pages = {179-194},

publisher = {EDP-Sciences},

title = {On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms},

url = {http://eudml.org/doc/273615},

volume = {17},

year = {2013},

}

TY - JOUR

AU - Cénac, Peggy

TI - On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms

JO - ESAIM: Probability and Statistics

PY - 2013

PB - EDP-Sciences

VL - 17

SP - 179

EP - 194

AB - 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.

LA - eng

KW - stochastic approximation algorithms; almost sure central limit theorem; martingale transforms; moments

UR - http://eudml.org/doc/273615

ER -

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