论文标题
相互作用的粒子系统和McKean-Vlasov SDE的Euler模拟，并在空间和相互作用中具有完全超级线性的生长漂移
Euler simulation of interacting particle systems and McKean-Vlasov SDEs with fully superlinear growth drifts in space and interaction
论文作者
论文摘要
在这项工作中，我们考虑了分裂式Euler类型方案（SSM）的收敛性，用于对相互作用的粒子随机微分方程（SDE）系统和McKean-Vlasov随机微分方程（MV-SDE）的数值模拟，并在空间和相互作用的互动组件中具有全面的超级线性增长，并且在散发和非co co co coe copchits coffff。 相互作用（或度量）组件中的超级线性增长源于具有超线性生长功能的卷积操作，尤其允许在具有多孔限制电势的颗粒状介质方程中应用。从方法论的角度来看，我们避免了完全的功能不平等参数（因为我们允许非恒定的非结合扩散图）。 该方案在Stepize中达到了一个近乎最佳的经典（路径空间）均方根错误率，$ 1/2- \ VAREPSILON $，对于$ \ VAREPSILON> 0 $，最佳速率$ 1/2 $在非PATH-PATCE-SPACE均值均值错误中。数值示例说明了所有发现。特别是，该测试引起了怀疑是否是针对此类问题的合适方法（卷积术语和非恒定扩散系数）。
We consider in this work the convergence of a split-step Euler type scheme (SSM) for the numerical simulation of interacting particle Stochastic Differential Equation (SDE) systems and McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with full super-linear growth in the spatial and the interaction component in the drift, and non-constant Lipschitz diffusion coefficient. The super-linear growth in the interaction (or measure) component stems from convolution operations with super-linear growth functions allowing in particular application to the granular media equation with multi-well confining potentials. From a methodological point of view, we avoid altogether functional inequality arguments (as we allow for non-constant non-bounded diffusion maps). The scheme attains, in stepsize, a near-optimal classical (path-space) root mean-square error rate of $1/2-\varepsilon$ for $\varepsilon>0$ and an optimal rate $1/2$ in the non-path-space mean-square error metric. Numerical examples illustrate all findings. In particular, the testing raises doubts if taming is a suitable methodology for this type of problem (with convolution terms and non-constant diffusion coefficients).
