Optimal strong convergence rate for a class of McKean-Vlasov SDEs with fast oscillating perturbation

被引：1

作者：

Li, Butong ^{[1
]}

Meng, Yongna ^{[1
]}

Sun, Xiaobin ^{[1
,2
]}

Yang, Ting ^{[1
,2
]}

机构：

[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China

[2] Jiangsu Normal Univ, Res Inst Math Sci, Xuzhou 221116, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2022年 / 191卷

基金：

中国国家自然科学基金;

关键词：

McKean-Vlasov stochastic differential equations; Slow-fast; Poisson equation; Strong convergence order; STOCHASTIC DIFFERENTIAL-EQUATIONS; AVERAGING PRINCIPLE; DRIVEN;

D O I：

10.1016/j.spl.2022.109662

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we consider the averaging principle for a class of McKean-Vlasov stochastic differential equations perturbed by a fast oscillating term. By using the technique of Poisson equation, we prove the occurrence of the averaging principle, i.e., the solution X epsilon converges to the solution X over line of the corresponding averaged equation in L2(& OHM;, C([0, T], Rn)) with the optimal convergence order 1/2. To the best of authors' knowledge, this is the first result about the strong averaging principle when the coefficients in the slow equation depends on the law of the fast component.(c) 2022 Elsevier B.V. All rights reserved.

引用

页数：10

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