发表机构
Nanyang Technological University; Bielefeld University; ETH Zurich（南洋理工大学; 比勒费尔德大学; 苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对带跳的McKean-Vlasov SDE提出MLP近似方法，证明其无维数灾难，计算成本呈多项式增长，且在维数达200的数值实验中验证了实用性。
AI 中文摘要
我们引入了带有限或无限活动跳的McKean-Vlasov随机微分方程（SDE）的多级Picard（MLP）近似。在对系数的Lipschitz连续性和可积性假设下，我们证明了MLP算法在近似McKean-Vlasov SDE的解时不会遭受维数灾难，这意味着其计算成本最多随SDE的状态空间维数和规定误差容限的倒数呈多项式增长。在两个数值实验中，我们证明了MLP算法对两个不同的McKean-Vlasov SDE（维数高达200）的实际适用性。
英文摘要
We introduce multilevel Picard (MLP) approximations of McKean-Vlasov stochastic differential equations (SDEs) with jumps of finite or infinite activity. Under Lipschitz and integrability assumptions on the coefficients, we show that the MLP algorithm does not suffer from the curse of dimensionality when approximating the solution of the McKean-Vlasov SDE. The latter means that its computational cost grows at most polynomially in both the state-space dimension of the SDE and the reciprocal of the prescribed error tolerance. In two numerical experiments, we demonstrate the practical applicability of the MLP algorithm for two different McKean-Vlasov SDEs in dimensions up to 200.
