Electronic Communications in Probability

Concentration bounds for stochastic approximations

Noufel Frikha and Stéphane Menozzi

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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.

Article information

Electron. Commun. Probab., Volume 17 (2012), paper no. 47, 15 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H35: Computational methods for stochastic equations [See also 65C30]
Secondary: 65C30: Stochastic differential and integral equations 65C05: Monte Carlo methods

Non asymptotic bounds Euler scheme Stochastic approximation algorithms Gaussian concentration

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Frikha, Noufel; Menozzi, Stéphane. Concentration bounds for stochastic approximations. Electron. Commun. Probab. 17 (2012), paper no. 47, 15 pp. doi:10.1214/ECP.v17-1952. https://projecteuclid.org/euclid.ecp/1465263180

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