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A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes

Conference paper
Authors Annika Lang
Published in 11th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2014, Leuven, Belgium, 6-11 April 2014
Volume 163
Pages 489-505
ISBN 978-3-319-33505-6
ISSN 2194-1009
Publication year 2015
Published at Department of Mathematical Sciences, Mathematical Statistics
Pages 489-505
Language en
Links dx.doi.org/10.1007/978-3-319-33507-...
Subject categories Mathematics, Applied mathematics, Probability Theory and Statistics

Abstract

It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many approximations of stochastic (ordinary) differential equations while it is recent research for stochastic partial differential equations. In this note it is shown how the availability of weak convergence results influences the number of samples in multilevel Monte Carlo schemes and therefore reduces the computational complexity of these schemes for a given accuracy of the approximations.

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