Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths

doi:10.1016/j.apnum.2018.03.006

	Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths
	Hong, Jialin1,2 ; Huang, Chuying 1,2; Wang, Xu 1,2
	2018-07-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	129 页码:120-136
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.
关键词	Rough path Hamiltonian system Symplectic Runge-Kutta method Implicit method Pathwlse convergence rate
DOI	10.1016/j.apnum.2018.03.006
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000430902800008
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30269
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.