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

文献类型：期刊论文

作者Cui, Jianbo3; Hong, Jialin1,2; Sun, Liying1,2
刊名STOCHASTIC PROCESSES AND THEIR APPLICATIONS
出版日期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
DOI10.1016/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
WOS记录号WOS:000654166300003
出版者ELSEVIER
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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