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In this paper we discuss the possibility of using multilevel Monte Carlo(MLMC) methods for weak approximation schemes. It turns out that by means of asimple coupling between consecutive time discretisation levels, one can achievethe same complexity gain as under the presence of a strong convergence. Weexemplify this general idea in the case of weak Euler scheme for L\'evy drivenstochastic differential equations, and show that, given a weak convergence oforder $\alpha\geq 1/2,$ the complexity of the corresponding "weak" MLMCestimate is of order $\varepsilon^{-2}\log ^{2}(\varepsilon).$ The numericalperformance of the new "weak" MLMC method is illustrated by several numericalexamples.

Multilevel path simulation for weak approximation schemes