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2012 Concentration bounds for stochastic approximations
Noufel Frikha, Stéphane Menozzi
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Electron. Commun. Probab. 17: 1-15 (2012). DOI: 10.1214/ECP.v17-1952


We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of an Euler like discretization scheme of some diffusion process at a fixed deterministic time and its empirical mean obtained by the Monte Carlo procedure. We then give some estimates concerning the deviation between the value at a given time-step of a stochastic approximation algorithm and its target. Under suitable assumptions both concentration bounds turn out to be Gaussian. The key tool consists in exploiting accurately the concentration properties of the increments of the schemes. Also, no specific non-degeneracy conditions are assumed.

An Erratum is available in ECP volume 17 paper number 60.


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Noufel Frikha. Stéphane Menozzi. "Concentration bounds for stochastic approximations." Electron. Commun. Probab. 17 1 - 15, 2012.


Accepted: 7 October 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1252.60065
MathSciNet: MR2988393
Digital Object Identifier: 10.1214/ECP.v17-1952

Primary: 60H35
Secondary: 65C05 , 65C30

Keywords: Euler scheme , Gaussian concentration , Non asymptotic bounds , Stochastic approximation algorithms

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