Electronic Journal of Probability

On Some non Asymptotic Bounds for the Euler Scheme

Stéphane Menozzi and Vincent Lemaire

Full-text: Open access

Abstract

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

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

Dates
Accepted: 26 October 2010
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819838

Digital Object Identifier
doi:10.1214/EJP.v15-814

Mathematical Reviews number (MathSciNet)
MR2735377

Zentralblatt MATH identifier
1225.60117

Subjects
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

Keywords
Non asymptotic Monte Carlo bounds Discretization schemes Gaussian concentration

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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