A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes
Paper in proceedings, 2016

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.

Stochastic heat equation

Weak error analysis

Multilevel Monte Carlo methods

Stochastic partial differential equations

Finite element approximations


Annika Lang

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

11th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2014, Leuven, Belgium, 6-11 April 2014

2194-1017 (eISSN)

Vol. 163 489-505

Subject Categories


Computational Mathematics

Probability Theory and Statistics


Basic sciences





More information