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.


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)
Full Text: DOI Euclid