Multi-level Monte Carlo methods with the truncated Euler-Maruyama scheme for stochastic differential equations

Guo, Qian and Liu, Wei and Mao, Xuerong and Zhan, Weijun (2017) Multi-level Monte Carlo methods with the truncated Euler-Maruyama scheme for stochastic differential equations. International Journal of Computer Mathematics. ISSN 0020-7160

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    Abstract

    The truncated Euler-Maruyama method is employed together with the Multi-level Monte Carlo method to approximate expectations of some functions of solutions to stochastic differential equations (SDEs). The convergence rate and the computational cost of the approximations are proved, when the coefficients of SDEs satisfy the local Lipschitz and Khasminskii-type conditions. Numerical examples are provided to demonstrate the theoretical results.