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On the Acceleration of the Multi-Level Monte Carlo Method

Part of: Probabilistic methods, simulation and stochastic differential equations Stochastic analysis

Published online by Cambridge University Press:  30 January 2018

Kristian Debrabant  and
Andreas Röβler
Kristian Debrabant*
Affiliation:
University of Southern Denmark
Andreas Röβler*
Affiliation:
Universität zu Lübeck
*
∗ Postal address: Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark.
∗∗ Postal address: Institut für Mathematik, Universität zu Lübeck, Ratzeburger Allee 160, D-23562 Lübeck, Germany. Email address: roessler@math.uni-luebeck.de
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Abstract

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The multi-level Monte Carlo method proposed by Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper a modified multi-level Monte Carlo estimator is proposed with significantly reduced computational costs. As the main result, it is proved that the modified estimator reduces the computational costs asymptotically by a factor (p / α)2 if weak approximation methods of orders α and p are applied in the case of computational costs growing with the same order as the variances decay.

Keywords

Multi-level Monte CarloMonte Carloweak approximationvariance reductionstochastic differential equation

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60H35: Computational methods for stochastic equations 65C20: Models, numerical methods 68U20: Simulation
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 307 - 322
Copyright
© Applied Probability Trust 

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