Belomestny, D.D.BelomestnyNagapetyan, TTNagapetyanShiryaev, V.V.Shiryaev2022-03-152022-03-152014https://publica.fraunhofer.de/handle/publica/413934In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify this general idea in the case of weak Euler scheme for L\'evy driven stochastic differential equations, and show that, given a weak convergence of order a>1/2, the complexity of the corresponding "weak" MLMC estimate is of order e−2log2(e). The numerical performance of the new "weak" MLMC method is illustrated by several numerical examples.en003006519paper