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A weak convergence theorem with application to the Robbins-Monro process

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Publication:1257283
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DOI10.1214/aop/1176995390zbMath0405.60019OpenAlexW2089964852MaRDI QIDQ1257283

Götz-Dietrich Kersting

Publication date: 1978

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176995390


zbMATH Keywords

Central Limit TheoremAsymptotic DistributionCoupling-ArgumentRobBins-Monro-Procedure


Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stochastic approximation (62L20)


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Asymptotic behavior of a modified stochastic optimization procedure in an averaging scheme ⋮ Central and functional central limit theorems for a class of urn models ⋮ Weak convergence of recursions ⋮ Asymptotic behavior for the Robbins–Monro process ⋮ Lower error bounds for the stochastic gradient descent optimization algorithm: sharp convergence rates for slowly and fast decaying learning rates ⋮ Weak convergence rates for stochastic approximation with application to multiple targets and simulated annealing ⋮ On Kersting's proof of the central limit theorem ⋮ A functional central limit theorem for a class of urn models



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