Electronic Journal of Probability

On Some non Asymptotic Bounds for the Euler Scheme

Stéphane Menozzi and Vincent Lemaire

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We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This Gaussian concentration is derived from a Gaussian upper bound of the density of the scheme and a modification of the so-called "Herbst argument" used to prove Logarithmic Sobolev inequalities. We eventually establish a Gaussian lower bound for the density of the scheme that emphasizes the concentration is sharp.

Article information

Electron. J. Probab., Volume 15 (2010), paper no. 53, 1645-1681.

Accepted: 26 October 2010
First available in Project Euclid: 1 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 60E15: Inequalities; stochastic orderings

Non asymptotic Monte Carlo bounds Discretization schemes Gaussian concentration

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Menozzi, Stéphane; Lemaire, Vincent. On Some non Asymptotic Bounds for the Euler Scheme. Electron. J. Probab. 15 (2010), paper no. 53, 1645--1681. doi:10.1214/EJP.v15-814. https://projecteuclid.org/euclid.ejp/1464819838

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