Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths
文献类型：期刊论文
| 作者 | Hong, Jialin1,2 ; Huang, Chuying1,2; Wang, Xu1,2
|
| 刊名 | APPLIED NUMERICAL MATHEMATICS
 |
| 出版日期 | 2018-07-01 |
| 卷号 | 129页码:120-136 |
| 关键词 | Rough path Hamiltonian system Symplectic Runge-Kutta method Implicit method Pathwlse convergence rate |
| ISSN号 | 0168-9274 |
| DOI | 10.1016/j.apnum.2018.03.006 |
| 英文摘要 | We consider Hamiltonian systems driven by multi-dimensional Gaussian processes in rough path sense, which include fractional Brownian motions with Hurst parameter H is an element of (1/4,1/2]. We prove that the phase flow preserves the symplectic structure almost surely and this property could be inherited by symplectic Runge-Kutta methods, which are implicit methods in general. If the vector fields satisfy some smoothness and boundedness conditions, we obtain the pathwise convergence rates of Runge-Kutta methods. When vector fields are linear, we get the solvability of the midpoint scheme for skew symmetric cases, and obtain its pathwise convergence rate. Numerical experiments verify our theoretical analysis. (C) 2018 IMACS. Published by 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:000430902800008 |
| 出版者 | ELSEVIER SCIENCE BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/30268]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Huang, Chuying |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Hong, Jialin,Huang, Chuying,Wang, Xu. Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths[J]. APPLIED NUMERICAL MATHEMATICS,2018,129:120-136. |
| APA | Hong, Jialin,Huang, Chuying,&Wang, Xu.(2018).Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths.APPLIED NUMERICAL MATHEMATICS,129,120-136. |
| MLA | Hong, Jialin,et al."Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths".APPLIED NUMERICAL MATHEMATICS 129(2018):120-136. |
入库方式： OAI收割
来源：数学与系统科学研究院
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