Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations

doi:10.1214/20-AIHP1087

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	Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations
	Rockner, Michael 1,2; Sun, Xiaobin 3,4; Xie, Yingchao 3,4
	2021-02-01
发表期刊	ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
ISSN	0246-0203
卷号	57 期号:1 页码:547-576
摘要	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.
关键词	Averaging principle McKean-Vlasov stochastic differential equations Slow-fast Poisson equation Strong convergence order
DOI	10.1214/20-AIHP1087
收录类别	SCI
语种	英语
资助项目	NSFC[11771187] ; NSFC[11931004] ; Priority Academic Program Development of Jiangsu Higher Education Institutions ; DFG[CRC 1283]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000628812400019
出版者	INST MATHEMATICAL STATISTICS-IMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58337
专题	中国科学院数学与系统科学研究院
通讯作者	Rockner, Michael
作者单位	1.Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China 4.Jiangsu Normal Univ, Res Inst Math Sci, Xuzhou 221116, Jiangsu, Peoples R China
推荐引用方式 GB/T 7714	Rockner, Michael,Sun, Xiaobin,Xie, Yingchao. Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations[J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,2021,57(1):547-576.
APA	Rockner, Michael,Sun, Xiaobin,&Xie, Yingchao.(2021).Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations.ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,57(1),547-576.
MLA	Rockner, Michael,et al."Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations".ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 57.1(2021):547-576.