Strong convergence rates in averaging principle for slow-fast McKean-Vlasov SPDEs
Strong convergence rates in averaging principle for slow-fast McKean-Vlasov SPDEs
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DOI：
10.1016/j.jde.2022.01.039
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发表时间：
2021-07
影响因子：
2.4
通讯作者：
Wei Hong;Shihu Li;Wei Liu
中科院分区：
文献类型：
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作者：
Wei Hong;Shihu Li;Wei Liu
本文研究了一类具有慢时标和快时标的McKean-Vlasov随机偏微分方程解的渐近性态。利用变分方法和经典的Khasminskii时间离散，我们证明了慢分量强收敛到相关的平均方程的解。特别地，还得到了相应的收敛速度。主要结果可用于证明各种McKean-Vlasov非线性随机偏微分方程的平均原理，如随机多孔介质型方程、随机p-Laplace型方程以及某些McKean-Vlasov随机微分方程.
In this paper, we aim to study the asymptotic behavior for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational approach and classical Khasminskii time discretization, we show that the slow component strongly converges to the solution of the associated averaged equation. In particular, the corresponding convergence rates are also obtained. The main results can be applied to demonstrate the averaging principle for various McKean-Vlasov nonlinear SPDEs such as stochastic porous media type equation, stochasticp-Laplace type equation and also some McKean-Vlasov stochastic differential equations.