The Multilevel Monte Carlo (MLMC) approach usually works well when estimating the expected value of a quantity which is a Lipschitz function of intermediate quantities, but if it is a discontinuous function it can lead to a much slower decay in the variance of the MLMC correction. This article reviews the literature on techniques which can be used to overcome this challenge in a variety of different contexts, and discusses recent developments using either a branching diffusion or adaptive sampling.

翻译：多层蒙特卡洛（MLMC）方法在估计中间量的Lipschitz函数期望值时通常效果良好，但当目标函数不连续时，MLMC校正项的方差衰减速度会显著降低。本文综述了在不同场景下应对这一挑战的相关文献技术，并讨论了利用分支扩散或自适应采样的最新研究进展。