CLT for approximating ergodic limit of SPDEs via a full discretization

doi:10.1016/j.spa.2022.11.015

	CLT for approximating ergodic limit of SPDEs via a full discretization
	Chen, Chuchu ; Dang, Tonghe 1; Hong, Jialin ; Zhou, Tau
刊名	STOCHASTIC PROCESSES AND THEIR APPLICATIONS
	2023-03-01
卷号	157 页码:1-41
关键词	Central limit theorem Stochastic partial differential equation Full discretization Poisson equation Ergodic limit
ISSN号	0304-4149
DOI	10.1016/j.spa.2022.11.015
英文摘要	In order to characterize quantitatively the fluctuations between the ergodic limit and the time -averaging estimator, we establish a central limit theorem for a full discretization of the parabolic SPDE, which shows that the normalized time-averaging estimator converges weakly to a normal distribution as the time stepsize tends to 0. A key ingredient in the proof is to extract an appropriate martingale difference series sum from the normalized time-averaging estimator via the Poisson equation, so that convergences of such a sum and the remainder are well balanced.(c) 2022 Elsevier B.V. All rights reserved.
资助项目	National key R&D Program of China ; National Natural Science Foundation of China ; Youth Innovation Promotion Association CAS, China ; [2020YFA0713701] ; [11971470] ; [11871068] ; [12031020] ; [12022118]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000899376200001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60512]
专题	中国科学院数学与系统科学研究院
通讯作者	Dang, Tonghe
作者单位	1.Chinese Acad Sci, ICMSEC, LSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Chen, Chuchu,Dang, Tonghe,Hong, Jialin,et al. CLT for approximating ergodic limit of SPDEs via a full discretization[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2023,157:1-41.
APA	Chen, Chuchu,Dang, Tonghe,Hong, Jialin,&Zhou, Tau.(2023).CLT for approximating ergodic limit of SPDEs via a full discretization.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,157,1-41.
MLA	Chen, Chuchu,et al."CLT for approximating ergodic limit of SPDEs via a full discretization".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 157(2023):1-41.