论文标题
McKean-Vlasov SDES的自适应Euler-Maruyama方案，具有超线性增长，并应用于平均场地Fitzhugh-Nagumo模型
An adaptive Euler-Maruyama scheme for McKean-Vlasov SDEs with super-linear growth and application to the mean-field FitzHugh-Nagumo model
论文作者
论文摘要
在本文中，我们介绍了McKean-Vlasov随机微分方程（SDE）的自适应Euler-Maruyama方案（SDES），假设在漂移和扩散系数上仅具有标准的单调性条件，而没有全球Lipschitz的连续性，而全球lipschitz连续性仅需要全球lipschitz ContimChitz ContimChitz ContimChitz Contimchitz Conturentus才能进行计量的组件。我们证明了离散流程的力矩稳定性和$ 1/2 $的强大收敛速度。几个数值示例围绕着菲茨胡格 - 纳古莫神经元的平均场模型，表明标准统一方案失败了，并且自适应方法在大多数情况下显示出较高的性能与驯服近似方案相比。此外，我们介绍并分析了一种具有线性测量依赖性的McKean-Vlasov Sdes的自适应米尔斯坦方案。
In this paper, we introduce adaptive Euler-Maruyama schemes for McKean-Vlasov stochastic differential equations (SDEs) assuming only a standard monotonicity condition on the drift and diffusion coefficients but no global Lipschitz continuity in the state variable for either, while global Lipschitz continuity is required for the measure component only. We prove moment stability of the discretised processes and a strong convergence rate of $1/2$. Several numerical examples, centred around a mean-field model for FitzHugh-Nagumo neurons, illustrate that the standard uniform scheme fails and that the adaptive approach shows in most cases superior performance to tamed approximation schemes. In addition, we introduce and analyse an adaptive Milstein scheme for a certain sub-class of McKean-Vlasov SDEs with linear measure-dependence of the drift.
