In this paper, we discuss the possibility of using multilevel Monte Carlo (MLMC) approach 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 schemes for Lévy-driven stochastic differential equations. The numerical performance of the new “weak” MLMC method is illustrated by several numerical examples.
"Multilevel path simulation for weak approximation schemes with application to Lévy-driven SDEs." Bernoulli 23 (2) 927 - 950, May 2017. https://doi.org/10.3150/15-BEJ764