We prove weak convergence of order one for a class of exponential based integrators for SDEs with non-globally Lipschtiz drift. Our analysis covers tamed versions of Geometric Brownian Motion (GBM) based methods as well as the standard exponential schemes. The numerical performance of both the GBM and exponential tamed methods through four different multi-level Monte Carlo techniques are compared. We observe that for linear noise the standard exponential tamed method requires severe restrictions on the stepsize unlike the GBM tamed method.

翻译：我们证明了一类针对具有非全局Lipschtiz漂移项的随机微分方程的指数型积分器具有一阶弱收敛性。我们的分析涵盖了基于几何布朗运动（GBM）的驯化方法以及标准指数格式。通过四种不同的多级蒙特卡洛技术，我们比较了GBM驯化方法与指数驯化方法的数值性能。我们观察到，对于线性噪声情形，与GBM驯化方法不同，标准指数驯化方法需要对步长施加严格限制。