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HIGH ORDER CONFORMAL SYMPLECTIC AND ERGODIC SCHEMES FOR THE STOCHASTIC LANGEVIN EQUATION VIA GENERATING FUNCTIONS
Hong, Jialin; Sun, Liying; Wang, Xu
2017
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume55Issue:6Pages:3006-3029
AbstractIn this paper, we consider the stochastic Langevin equation with additive noises, which possesses both conformal symplectic geometric structure and ergodicity. We propose a methodology of constructing high weak order conformal symplectic schemes by converting the equation into an equivalent autonomous stochastic Hamiltonian system and modifying the associated generating function. To illustrate this approach, we construct a specific second order numerical scheme and prove that its symplectic form dissipates exponentially. Moreover, for the linear case, the proposed scheme is also shown to inherit the ergodicity of the original system, and the temporal average of the numerical solution is a proper approximation of the ergodic limit over long time. Numerical experiments are given to verify these theoretical results.
Keywordstochastic Langevin equation conformal symplectic scheme generating function ergodicity weak convergence
DOI10.1137/17M111691X
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[11290142] ; National Natural Science Foundation of China[91630312]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000418663500020
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/27097
Collection计算数学与科学工程计算研究所
Corresponding AuthorSun, Liying
AffiliationChinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Hong, Jialin,Sun, Liying,Wang, Xu. HIGH ORDER CONFORMAL SYMPLECTIC AND ERGODIC SCHEMES FOR THE STOCHASTIC LANGEVIN EQUATION VIA GENERATING FUNCTIONS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2017,55(6):3006-3029.
APA Hong, Jialin,Sun, Liying,&Wang, Xu.(2017).HIGH ORDER CONFORMAL SYMPLECTIC AND ERGODIC SCHEMES FOR THE STOCHASTIC LANGEVIN EQUATION VIA GENERATING FUNCTIONS.SIAM JOURNAL ON NUMERICAL ANALYSIS,55(6),3006-3029.
MLA Hong, Jialin,et al."HIGH ORDER CONFORMAL SYMPLECTIC AND ERGODIC SCHEMES FOR THE STOCHASTIC LANGEVIN EQUATION VIA GENERATING FUNCTIONS".SIAM JOURNAL ON NUMERICAL ANALYSIS 55.6(2017):3006-3029.
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