DISCRETE GRADIENT APPROACH TO STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY

doi:10.1137/090771880

	DISCRETE GRADIENT APPROACH TO STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY
	Hong, Jialin; Zhai, Shuxing; Zhang, Jingjing
	2011
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	49 期号:5 页码:2017-2038
摘要	General autonomous stochastic differential equations (SDEs) driven by one-dimensional Brownian motion in the Stratonovich sense with a conserved quantity I(y) are considered. Relying on this conserved quantity, an equivalent "skew gradient" (SG) form of original SDEs is constructed. With the aim of constructing conserved numerical methods, direct discrete gradient approaches which approximate directly the SG system lead to two conserved methods. In indirect discrete gradient approaches, we first split the SG system into subsystems which preserve the original conserved quantity, then apply direct discrete gradient approaches to subsystems to produce two composition schemes. The mean-square convergence of order 1 for these four methods depends on the assumptions that the coefficients of SDEs are Lipschitz continuous with bounded second moments along the solution of SDEs, are twice continuous differentiable, and have derivatives that are uniformly bounded. Three numerical experiments are presented to verify our theoretical analysis and show the advantages of these methods.
关键词	stochastic differential equation in the Stratonovich sense conserved quantity discrete gradient splitting technique mean-square convergence
DOI	10.1137/090771880
语种	英语
资助项目	Director Innovation Foundation of ICMSEC ; AMSS ; Foundation of CAS ; NNSFC[60771054] ; Special Funds for Major State Basic Research Projects of China[2005CB321701]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000296605600013
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/12052
专题	计算数学与科学工程计算研究所
通讯作者	Hong, Jialin
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Hong, Jialin,Zhai, Shuxing,Zhang, Jingjing. DISCRETE GRADIENT APPROACH TO STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2011,49(5):2017-2038.
APA	Hong, Jialin,Zhai, Shuxing,&Zhang, Jingjing.(2011).DISCRETE GRADIENT APPROACH TO STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY.SIAM JOURNAL ON NUMERICAL ANALYSIS,49(5),2017-2038.
MLA	Hong, Jialin,et al."DISCRETE GRADIENT APPROACH TO STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY".SIAM JOURNAL ON NUMERICAL ANALYSIS 49.5(2011):2017-2038.