In this paper, we investigate the properties of standard and multilevel Monte Carlo methods for weak approximation of solutions of stochastic differential equations (SDEs) driven by the infinite-dimensional Wiener process and Poisson random measure with Lipschitz payoff function. The error of the truncated dimension randomized numerical scheme, which is determined by two parameters, i.e grid density $n \in \mathbb{N}_{+}$ and truncation dimension parameter $M \in \mathbb{N}_{+},$ is of the order $n^{-1/2}+\delta(M)$ such that $\delta(\cdot)$ is positive and decreasing to $0$. We derive complexity model and provide proof for the upper complexity bound of the multilevel Monte Carlo method which depends on two increasing sequences of parameters for both $n$ and $M.$ The complexity is measured in terms of upper bound for mean-squared error and compared with the complexity of the standard Monte Carlo algorithm. The results from numerical experiments as well as Python and CUDA C implementation are also reported.

翻译：本文研究由无穷维维纳过程和泊松随机测度驱动的随机微分方程弱近似解的标准蒙特卡洛与多层蒙特卡洛方法性质，其中支付函数满足Lipschitz条件。截断维随机数值格式的误差由网格密度$n \in \mathbb{N}_{+}$和截断维参数$M \in \mathbb{N}_{+}$两个参数决定，其误差阶为$n^{-1/2}+\delta(M)$，其中$\delta(\cdot)$为正且递减至$0$。我们推导了复杂度模型，并证明了取决于$n$和$M$两个递增参数序列的多层蒙特卡洛方法的上界复杂度。复杂度以均方误差上界进行度量，并与标准蒙特卡洛算法的复杂度进行对比。文中还报告了数值实验结果及Python与CUDA C实现。