Non-asymptotic error bounds for The Multilevel Monte Carlo Euler method applied to SDEs with constant diffusion coefficient - Archive ouverte HAL Access content directly
Journal Articles Electronic Journal of Probability Year : 2019

Non-asymptotic error bounds for The Multilevel Monte Carlo Euler method applied to SDEs with constant diffusion coefficient

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 obtain Gaussian-type concentration. 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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Dates and versions

hal-01577874 , version 1 (13-02-2024)

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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. Electronic Journal of Probability, 2019, 24 (12), pp.1-34. ⟨10.1214/19-EJP271⟩. ⟨hal-01577874⟩
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