HIGH ORDER CONFORMAL SYMPLECTIC AND ERGODIC SCHEMES FOR THE STOCHASTIC LANGEVIN EQUATION VIA GENERATING FUNCTIONS

doi:10.1137/17M111691X

	HIGH ORDER CONFORMAL SYMPLECTIC AND ERGODIC SCHEMES FOR THE STOCHASTIC LANGEVIN EQUATION VIA GENERATING FUNCTIONS
	Hong, Jialin; Sun, Liying; Wang, Xu
	2017
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	55 期号:6 页码:3006-3029
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.
关键词	stochastic Langevin equation conformal symplectic scheme generating function ergodicity weak convergence
DOI	10.1137/17M111691X
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[11290142] ; National Natural Science Foundation of China[91630312]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000418663500020
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/27097
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.