论文标题
McKean-Vlasov方程的Wasserstein空间上的泊松方程和扩散近似值
Poisson equation on Wasserstein space and diffusion approximations for McKean-Vlasov equation
论文作者
论文摘要
我们考虑具有多时间尺度电位的完全耦合的McKean-Vlasov方程，所有系数都取决于慢速组件和快速运动的分布。通过研究瓦斯汀空间上非线性泊松方程溶液的平滑度，我们得出了渐近极限以及缓慢过程的收敛性的定量误差估计值。在泊松方程解的测量参数中包含衍生物的额外均质漂移项出现在极限中，这似乎是新的，对于涉及快速分布的系统是独一无二的。
We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the non-linear Poisson equation on Wasserstein space, we derive the asymptotic limit as well as the quantitative error estimate of the convergence for the slow process. Extra homogenized drift term containing derivative in the measure argument of the solution of the Poisson equation appears in the limit, which seems to be new and is unique for systems involving the fast distribution.
