论文标题
平均DDSDE的强度和弱收敛性与单数漂移
Strong and weak convergence for averaging principle of DDSDE with singular drift
论文作者
论文摘要
在本文中，我们研究了与分布相关的随机微分方程的平均原理，其局部$ l^p $空间的漂移。使用Zvonkin的转换和对Kolmogorov方程的解决方案的估计，我们证明原始系统的解决方案随着时间尺度$ \ eps $的零，将原始系统的解决方案强烈而微弱地收敛到平均系统的解决方案。此外，我们分别获得了分别取决于$ p $的强和弱收敛速度的费率。
In this paper, we study the averaging principle for distribution dependent stochastic differential equations with drift in localized $L^p$ spaces. Using Zvonkin's transformation and estimates for solutions to Kolmogorov equations, we prove that the solutions of the original system strongly and weakly converge to the solution of the averaged system as the time scale $\eps$ goes to zero. Moreover, we obtain rates of the strong and weak convergence that depend on $p$ respectively.
