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In this paper, the truncated Euler-Maruyama (EM) method is employed togetherwith the Multi-level Monte Carlo (MLMC) method to approximate the expectationsof functions of solutions to stochastic differential equations (SDEs). Theconvergence rate and the computational cost of the approximations using thetruncated EM method with the MLMC method are proved when the coefficients ofSDEs fulfill the local Lipschitz and Khasminskii-type conditions. Numericalexamples are given to demonstrate the theoretical results.

Multi-level Monte Carlo methods with the Truncated Euler-Maruyama Scheme for Stochastic Differential Equations