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It is a well-known rule of thumb that approximations of stochastic partialdifferential equations have essentially twice the order of weak convergencecompared to the corresponding order of strong convergence. This is alreadyknown for many approximations of stochastic (ordinary) differential equationswhile it is recent research for stochastic partial differential equations. Inthis note it is shown how the availability of weak convergence resultsinfluences the number of samples in multilevel Monte Carlo schemes andtherefore reduces the computational complexity of these schemes for a givenaccuracy of the approximations.

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