Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients

doi:10.1016/j.spa.2020.12.003

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	Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients
	Cui, Jianbo 1; Hong, Jialin 2,3; Sun, Liying 2,3
	2021-04-01
发表期刊	STOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN	0304-4149
卷号	134 页码:55-93
摘要	We propose a full discretization to approximate the invariant measure numerically for parabolic stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients. We present a priori estimates and regularity estimates of the numerical solution via a variational approach and Malliavin calculus. Under certain hypotheses, we present the time-independent regularity estimates for the corresponding Kolmogorov equation and the time-independent weak convergence analysis for the full discretization. Furthermore, we show that the V-uniformly ergodic invariant measure of the original system is approximated by this full discretization with weak convergence rate. Numerical experiments verify theoretical findings. (C) 2020 Elsevier B.V. All rights reserved.
关键词	Weak convergence Invariant measure Kolmogorov equation Malliavin calculus
DOI	10.1016/j.spa.2020.12.003
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[11290142]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000654166300003
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58693
专题	中国科学院数学与系统科学研究院
通讯作者	Cui, Jianbo
作者单位	1.Georgia Tech, Sch Math, Atlanta, GA 30332 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Cui, Jianbo,Hong, Jialin,Sun, Liying. Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2021,134:55-93.
APA	Cui, Jianbo,Hong, Jialin,&Sun, Liying.(2021).Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,134,55-93.
MLA	Cui, Jianbo,et al."Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 134(2021):55-93.