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In this paper, we investigate the properties of standard and multilevel MonteCarlo methods for weak approximation of solutions of stochastic differentialequations (SDEs) driven by the infinite-dimensional Wiener process and Poissonrandom measure with the Lipschitz payoff function. The error of the truncateddimension 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 $0$. The paper introduces thecomplexity model and provides proof for the upper complexity bound of themultilevel Monte Carlo method which depends on two increasing sequences ofparameters for both $n$ and $M.$ The complexity is measured in terms of upperbound for mean-squared error and compared with the complexity of the standardMonte Carlo algorithm. The results from numerical experiments as well as Pythonand CUDA C implementation are also reported.

A multilevel Monte Carlo algorithm for SDEs driven by countably dimensional Wiener process and Poisson random measure