# On some Non Asymptotic Bounds for the Euler Scheme

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.
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Journal articles
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2010, pp.1645-1681. <https://projecteuclid.org/euclid.ejp/1464819838>
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https://hal.archives-ouvertes.fr/hal-00445494
Contributor : Stephane Menozzi <>
Submitted on : Friday, January 8, 2010 - 4:35:37 PM
Last modification on : Tuesday, October 11, 2016 - 2:33:21 PM
Document(s) archivé(s) le : Thursday, June 17, 2010 - 8:25:27 PM

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### Identifiers

• HAL Id : hal-00445494, version 1
• ARXIV : 1001.1347

### Citation

Vincent Lemaire, Stephane Menozzi. On some Non Asymptotic Bounds for the Euler Scheme. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2010, pp.1645-1681. <https://projecteuclid.org/euclid.ejp/1464819838>. <hal-00445494>

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