Multi-level Monte Carlo methods with the Truncated Euler-Maruyama Scheme for Stochastic Differential Equations
For researchers in computational stochastic differential equations, this provides a theoretical foundation for an efficient simulation method under mild conditions.
This paper proves convergence rates and computational costs for combining the truncated Euler-Maruyama method with Multi-level Monte Carlo to approximate expectations of SDE solutions under local Lipschitz and Khasminskii-type conditions, supported by numerical examples.
In this paper, the truncated Euler-Maruyama (EM) method is employed together with the Multi-level Monte Carlo (MLMC) method to approximate the expectations of functions of solutions to stochastic differential equations (SDEs). The convergence rate and the computational cost of the approximations using the truncated EM method with the MLMC method are proved when the coefficients of SDEs fulfill the local Lipschitz and Khasminskii-type conditions. Numerical examples are given to demonstrate the theoretical results.