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 CONSERVATIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY Chen, Chuchu1,2; Cohen, David3; Hong, Jialin1 2016 Source Publication INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING ISSN 1705-5105 Volume 13Issue:3Pages:435-456 Abstract This paper proposes a novel conservative method for the numerical approximation of general stochastic differential equations in the Stratonovich sense with a conserved quantity. We show that the mean-square order of the method is 1 if noises are commutative and that the weak order is 1 in the general case. Since the proposed method may need the computation of a deterministic integral, we analyse the effect of the use of quadrature formulas on the convergence orders. Furthermore, based on the splitting technique of stochastic vector fields, we construct conservative composition methods with similar orders as the above method. Finally, numerical experiments are presented to support our theoretical results. Keyword Stochastic differential equations invariants conservative methods stochastic geometric numerical integration quadrature formula splitting technique mean-square convergence order weak convergence order Language 英语 Funding Project National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[11290142] ; UMIT Research Lab at Umea University ; Swedish Research Council (VR) WOS Research Area Mathematics WOS Subject Mathematics, Applied ; Mathematics WOS ID WOS:000376450900006 Publisher ISCI-INST SCIENTIFIC COMPUTING & INFORMATION Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/22807 Collection 计算数学与科学工程计算研究所 Corresponding Author Chen, Chuchu; Cohen, David; Hong, Jialin Affiliation 1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing, Peoples R China2.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA3.Umea Univ, Matemat & Matemat Stat, S-90187 Umea, Sweden Recommended CitationGB/T 7714 Chen, Chuchu,Cohen, David,Hong, Jialin. CONSERVATIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,2016,13(3):435-456. APA Chen, Chuchu,Cohen, David,&Hong, Jialin.(2016).CONSERVATIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY.INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,13(3),435-456. MLA Chen, Chuchu,et al."CONSERVATIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY".INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING 13.3(2016):435-456.
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