论文标题
米尔斯坦方案的一阶融合用于McKean-Vlasov方程和相互作用的粒子系统
First order convergence of Milstein schemes for McKean-Vlasov equations and interacting particle systems
论文作者
论文摘要
在本文中，我们为McKean-Vlasov随机微分方程（McKean-vlasov SDES）得出了完全可实现的一阶时间步变方案，从而使状态分量的超级线性增长允许漂移术语。我们提出了米尔斯坦方案，用于与McKean-vlasov方程相关的时间限制的相互作用粒子系统，并证明阶命令1和力矩稳定性的强烈收敛性，如果只有单方面的Lipschitz条件，则可以驯服漂移。为了获得强劲的收敛速率的主要结果，我们利用微积分在有限的二阶矩时概率度量的空间。此外，提出了支持我们理论发现的数值示例。
In this paper, we derive fully implementable first order time-stepping schemes for McKean--Vlasov stochastic differential equations (McKean--Vlasov SDEs), allowing for a drift term with super-linear growth in the state component. We propose Milstein schemes for a time-discretised interacting particle system associated with the McKean--Vlasov equation and prove strong convergence of order 1 and moment stability, taming the drift if only a one-sided Lipschitz condition holds. To derive our main results on strong convergence rates, we make use of calculus on the space of probability measures with finite second order moments. In addition, numerical examples are presented which support our theoretical findings.
