HIGH ORDER CONFORMAL SYMPLECTIC AND ERGODIC SCHEMES FOR THE STOCHASTIC LANGEVIN EQUATION VIA GENERATING FUNCTIONS
文献类型：期刊论文
| 作者 | Hong, Jialin ; Sun, Liying; Wang, Xu
|
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2017 |
| 卷号 | 55期号:6页码:3006-3029 |
| 关键词 | stochastic Langevin equation conformal symplectic scheme generating function ergodicity weak convergence |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/17M111691X |
| 英文摘要 | In 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. |
| 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[11290142] ; National Natural Science Foundation of China[91630312] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000418663500020 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/27096]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Sun, Liying |
| 作者单位 | Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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