# Multilevel Richardson-Romberg Extrapolation

@article{Lemaire2014MultilevelRE,
title={Multilevel Richardson-Romberg Extrapolation},
author={Vincent Lemaire and Gilles Pag{\e}s},
journal={Derivatives eJournal},
year={2014}
}`
• Published 6 January 2014
• Mathematics
• Derivatives eJournal
We propose and analyze a Multilevel Richardson-Romberg ($MLRR$) estimator which combines the higher order bias cancellation of the Multistep Richardson-Romberg ($MSRR$) method introduced in [Pag07] and the variance control resulting from the stratification in the Multilevel Monte Carlo ($MLMC$) method (see [Hei01, Gil08]). Thus we show that in standard frameworks like discretization schemes of diffusion processes an assigned quadratic error $\varepsilon$ can be obtained with our ($MLRR… ## Figures and Tables from this paper • Computer Science NAA • 2016 This work revisits the ML2R and MLMC estimators in the framework of the antithetic approach, thereby allowing us to remove the bias whilst preserving the optimal complexity when using Milstein scheme. • Mathematics The Annals of Applied Probability • 2018 We investigate a weighted Multilevel Richardson-Romberg extrapolation for the ergodic approximation of invariant distributions of diffusions adapted from the one introduced in~[Lemaire-Pages, 2013] • Mathematics Monte Carlo Methods Appl. • 2017 A Strong Law of Large Numbers and a Central Limit Theorem are investigated and some typical fields of applications: discretization schemes of diffusions and nested Monte Carlo are applied. • Computer Science, Mathematics • 2022 In this paper, we propose and analyze a novel combination of multilevel Richardson-Romberg (ML2R) and importance sampling algorithm, with the aim of reducing the overall computational time, while • Mathematics • 2019 Let$\mu\in \mathcal{P}_2(\mathbb R^d)$, where$\mathcal{P}_2(\mathbb R^d)$denotes the space of square integrable probability measures, and consider a Borel-measurable function$\Phi:\mathcal
This thesis is dedicated to the study of the strong convergence properties of the Ninomiya-Victoir scheme, which is based on the resolution of $d+1$ ordinary differential equations (ODEs) at each
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This work combines multilevel Monte Carlo methods with importance sampling (IS) to estimate rare event quantities that can be expressed as the expectation of a Lipschitz observable of the solution to
• Computer Science
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• 2016
A novel sampling algorithm that aims to reduce the bias of SG-MCMC while keeping the variance at a reasonable level is proposed and it is shown that SGRRLD is asymptotically consistent, satisfies a central limit theorem, and its non-asymptotic bias and the mean squared-error can be bounded.
• Computer Science
• 2016
A novel sampling algorithm that aims to reduce the bias of SG-MCMC while keeping the variance at a reasonable level is proposed and it is shown that SGRRLD is asymptotically consistent, satisfies a central limit theorem, and its non-asymptotic bias and the mean squared-error can be bounded.

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