论文标题
米尔斯坦方案和延迟McKean-Vlasov方程和相互作用的粒子系统的摩尔斯坦计划和反遗传多级蒙特卡洛采样
Milstein schemes and antithetic multilevel Monte Carlo sampling for delay McKean-Vlasov equations and interacting particle systems
论文作者
论文摘要
在本文中，我们首先得出了与点延迟麦基恩 - 维拉索夫随机微分方程（McKean-vlasov SDES）相关的相互作用粒子系统，可能具有漂移项在状态分量中具有超线性生长。我们证明了阶稳定稳定性的强烈收敛性，利用了有限的二阶矩概率测量空间上的变异微积分的技术。然后，我们引入了一种反基础的多级米尔斯坦方案，该方案为解决方案的预期功能提供了最佳的复杂性估计器，以延迟McKean-Vlasov方程，而无需模拟Lévy区域。
In this paper, we first derive Milstein schemes for an interacting particle system associated with point delay McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs), possibly with a drift term exhibiting super-linear growth in the state component. We prove strong convergence of order one and moment stability, making use of techniques from variational calculus on the space of probability measures with finite second order moments. Then, we introduce an antithetic multilevel Milstein scheme, which leads to optimal complexity estimators for expected functionals of solutions to delay McKean-Vlasov equations without the need to simulate Lévy areas.
