论文标题
相互作用的粒子系统和McKean-vlasov SDE的明确米尔斯坦型方案，具有常见的噪声和非差异漂移系数
An explicit Milstein-type scheme for interacting particle systems and McKean--Vlasov SDEs with common noise and non-differentiable drift coefficients
论文作者
论文摘要
我们为McKean- Vlasov随机微分方程和相关的高维相互作用粒子系统与常见的噪声提出了一个明确的漂移米尔斯坦方案。通过在空间和度量中使用漂移随机性步骤，我们在降低的漂移系数上的规律性假设下，建立了该方案的强收敛速度为$ 1 $：不需要在空间或测量衍生物中（例如，狮子会/fréchet）中的经典（Euclidean）衍生物。主要结果是通过丰富先前用于标准SDE的数值方案的双态性和一致性的概念来确定的。我们引入了某些Spijker型规范（以及相关的Banach空间），以处理正在分析的随机系统中存在的粒子的相互作用。提供了有关该计划复杂性的讨论。
We propose an explicit drift-randomised Milstein scheme for both McKean--Vlasov stochastic differential equations and associated high-dimensional interacting particle systems with common noise. By using a drift-randomisation step in space and measure, we establish the scheme's strong convergence rate of $1$ under reduced regularity assumptions on the drift coefficient: no classical (Euclidean) derivatives in space or measure derivatives (e.g., Lions/Fréchet) are required. The main result is established by enriching the concepts of bistability and consistency of numerical schemes used previously for standard SDE. We introduce certain Spijker-type norms (and associated Banach spaces) to deal with the interaction of particles present in the stochastic systems being analysed. A discussion of the scheme's complexity is provided.
