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Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients
Cui, Jianbo1; Hong, Jialin2,3; Sun, Liying2,3
2021-04-01
Source PublicationSTOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN0304-4149
Volume134Pages:55-93
AbstractWe 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.
KeywordWeak convergence Invariant measure Kolmogorov equation Malliavin calculus
DOI10.1016/j.spa.2020.12.003
Indexed BySCI
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000654166300003
PublisherELSEVIER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/58693
Collection中国科学院数学与系统科学研究院
Corresponding AuthorCui, Jianbo
Affiliation1.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
Recommended Citation
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.
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