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

	Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients
	Cui, Jianbo 3; Hong, Jialin 1,2; Sun, Liying 1,2
刊名	STOCHASTIC PROCESSES AND THEIR APPLICATIONS
	2021-04-01
卷号	134 页码:55-93
关键词	Weak convergence Invariant measure Kolmogorov equation Malliavin calculus
ISSN号	0304-4149
DOI	10.1016/j.spa.2020.12.003
英文摘要	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.
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
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000654166300003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58692]
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Georgia Tech, Sch Math, Atlanta, GA 30332 USA
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.