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CONSERVATIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY
Chen, Chuchu1,2; Cohen, David3; Hong, Jialin1
2016
Source PublicationINTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
ISSN1705-5105
Volume13Issue:3Pages:435-456
AbstractThis 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.
KeywordStochastic differential equations invariants conservative methods stochastic geometric numerical integration quadrature formula splitting technique mean-square convergence order weak convergence order
Language英语
Funding ProjectNational 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 AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000376450900006
PublisherISCI-INST SCIENTIFIC COMPUTING & INFORMATION
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/22807
Collection计算数学与科学工程计算研究所
Corresponding AuthorChen, Chuchu; Cohen, David; Hong, Jialin
Affiliation1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing, Peoples R China
2.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
3.Umea Univ, Matemat & Matemat Stat, S-90187 Umea, Sweden
Recommended Citation
GB/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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