KMS Of Academy of mathematics and systems sciences, CAS
| 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 Publication | STOCHASTIC PROCESSES AND THEIR APPLICATIONS
 |
| ISSN | 0304-4149 |
| Volume | 134Pages:55-93 |
| Abstract | 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. |
| Keyword | Weak convergence Invariant measure Kolmogorov equation Malliavin calculus |
| DOI | 10.1016/j.spa.2020.12.003 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Statistics & Probability |
| WOS ID | WOS:000654166300003 |
| Publisher | ELSEVIER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58693 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Cui, Jianbo |
| Affiliation | 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 |
| 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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