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2019 Non-asymptotic error bounds for the multilevel Monte Carlo Euler method applied to SDEs with constant diffusion coefficient
Benjamin Jourdain, Ahmed Kebaier
Electron. J. Probab. 24(none): 1-34 (2019). DOI: 10.1214/19-EJP271

Abstract

In this paper, we are interested in deriving non-asymptotic error bounds for the multilevel Monte Carlo method. As a first step, we deal with the explicit Euler discretization of stochastic differential equations with a constant diffusion coefficient. We prove that, as long as the deviation is below an explicit threshold, a Gaussian-type concentration inequality optimal in terms of the variance holds for the multilevel estimator. To do so, we use the Clark-Ocone representation formula and derive bounds for the moment generating functions of the squared difference between a crude Euler scheme and a finer one and of the squared difference of their Malliavin derivatives.

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Benjamin Jourdain. Ahmed Kebaier. "Non-asymptotic error bounds for the multilevel Monte Carlo Euler method applied to SDEs with constant diffusion coefficient." Electron. J. Probab. 24 1 - 34, 2019. https://doi.org/10.1214/19-EJP271

Information

Received: 4 September 2017; Accepted: 23 January 2019; Published: 2019
First available in Project Euclid: 20 February 2019

zbMATH: 07055650
MathSciNet: MR3916332
Digital Object Identifier: 10.1214/19-EJP271

Subjects:
Primary: 60H07, 60H35, 65C05, 65C30

JOURNAL ARTICLE
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Vol.24 • 2019
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