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Multilevel path simulation for weak approximation schemes with application to Lévy-driven SDEs. (English) Zbl 1416.60069

Summary: 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.

MSC:

60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60G51 Processes with independent increments; Lévy processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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