论文标题
多尺度McKean-Vlasov SDE的扩散近似通过不同的方法
Diffusion Approximation for Multi-Scale McKean-Vlasov SDEs Through Different Methods
论文作者
论文摘要
在本文中，我们旨在研究多尺度McKean-Vlasov随机微分方程的扩散近似。更准确地说，我们证明了慢速过程$ x^\ varepsilon $在$ c（[0，t]; \ mathbb {r}^n）中的薄弱收敛性，趋向于限制过程$ x $，这是分布依赖分布的随机微分方程的解决方案，与原始方程相比，一些新的漂移和扩散术语与原始方程相比出现。主要贡献是使用两种不同的方法分别明确表征限制方程。通过这两种方法，在限制方程中获得的扩散系数具有不同的形式，但是可以通过比较来断言它们是必不可少的。
In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$ towards the limiting process $X$ that is the solution of a distribution dependent stochastic differential equation in which some new drift and diffusion terms compared to the original equation appear. The main contribution is to use two different methods to explicitly characterize the limiting equations respectively. The obtained diffusion coefficients in the limiting equations have different form through these two methods, however it will be asserted that they are essential the same by a comparison.
