Open Access
Translator Disclaimer
2010 On Some non Asymptotic Bounds for the Euler Scheme
Stéphane Menozzi, Vincent Lemaire
Author Affiliations +
Electron. J. Probab. 15: 1645-1681 (2010). DOI: 10.1214/EJP.v15-814

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.

Citation

Download Citation

Stéphane Menozzi. Vincent Lemaire. "On Some non Asymptotic Bounds for the Euler Scheme." Electron. J. Probab. 15 1645 - 1681, 2010. https://doi.org/10.1214/EJP.v15-814

Information

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

zbMATH: 1225.60117
MathSciNet: MR2735377
Digital Object Identifier: 10.1214/EJP.v15-814

Subjects:
Primary: 60H35
Secondary: 60E15, 65C05, 65C30

JOURNAL ARTICLE
37 PAGES


SHARE
Vol.15 • 2010
Back to Top