The paper introduces a new weak approximation algorithm for stochastic differential equations (SDEs) of McKean–Vlasov type. The arbitrary order discretization scheme is available and is given using Malliavin weights, certain polynomial weights of Brownian motion, which play a role as correction of the approximation. The new weak approximation scheme works even if the test function is not smooth. In other words, the expectation of irregular functionals of McKean–Vlasov SDEs such as probability distribution functions are approximated through the proposed scheme. The effectiveness of the higher order scheme is confirmed by numerical examples for McKean–Vlasov SDEs including the Kuramoto model.

本文介绍了一种新的弱逼近算法，用于 McKean-Vlasov 类型的随机微分方程 (SDE)。可以使用任意阶离散化方案，并使用 Malliavin 权重（布朗运动的某些多项式权重）给出，这些权重起到修正近似的作用。即使测试函数不平滑，新的弱逼近方案也能工作。换句话说，McKean-Vlasov SDE 的不规则函数的期望，例如概率分布函数，通过所提出的方案来近似。包括 Kuramoto 模型在内的 McKean-Vlasov SDE 的数值例子证实了高阶方案的有效性。