Strong convergence order for slow–fast McKean–Vlasov stochastic differential equations
Strong convergence order for slow–fast McKean–Vlasov stochastic differential equations
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DOI：
10.1214/20-aihp1087
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
M. Rockner;Xiaobin Sun;Yingchao Xie
中科院分区：
文献类型：
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作者：
M. Rockner;Xiaobin Sun;Yingchao Xie
本文研究了一类具有慢时标和快时标的McKean-Vlasov随机微分方程的平均原理。在适当的系数假设下，利用时间离散方法证明了慢分量强收敛于相应的平均方程的解，且收敛阶为1/3。在系数正则性较强的条件下，利用Poisson方程的技巧将阶数提高到1/2阶，这是一般情况下强收敛的最优阶数.
In this paper, we consider the averaging principle for a class of McKean-Vlasov stochastic differential equations with slow and fast time-scales. Under some proper assumptions on the coefficients, we first prove that the slow component strongly converges to the solution of the corresponding averaged equation with convergence order $1/3$ using the approach of time discretization. Furthermore, under stronger regularity conditions on the coefficients, we use the technique of Poisson equation to improve the order to $1/2$, which is the optimal order of strong convergence in general.