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APPROXIMATING STOCHASTIC EVOLUTION EQUATIONS WITH ADDITIVE WHITE AND ROUGH NOISES
Cao, Yanzhao1,2; Hong, Jialin3; Liu, Zhihui3
2017
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume55Issue:4Pages:1958-1981
AbstractIn this paper, we analyze Galerkin approximations for stochastic evolution equations driven by an additive Gaussian noise which is temporally white and spatially fractional with Hurst index less than or equal to 1/2. First we regularize the noise by the Wong-Zakai approximation and obtain its optimal order of convergence. Then we apply the Galerkin method to discretize the stochastic evolution equations with regularized noises. Optimal error estimates are obtained for the Galerkin approximations. In particular, our error estimates remove an infinitesimal factor which appears in the error estimates of various numerical methods for stochastic evolution equations in existing literatures.
Keywordstochastic evolution equation fractional Brownian motion Wong-Zakai approximation Galerkin approximation
DOI10.1137/16M1056122
Language英语
Funding ProjectNational Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[11290142] ; U.S. National Science Foundation[DMS1620150]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000408925300017
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26458
Collection计算数学与科学工程计算研究所
Affiliation1.Jilin Univ, Sch Math, Changchun, Jilin, Peoples R China
2.Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Cao, Yanzhao,Hong, Jialin,Liu, Zhihui. APPROXIMATING STOCHASTIC EVOLUTION EQUATIONS WITH ADDITIVE WHITE AND ROUGH NOISES[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2017,55(4):1958-1981.
APA Cao, Yanzhao,Hong, Jialin,&Liu, Zhihui.(2017).APPROXIMATING STOCHASTIC EVOLUTION EQUATIONS WITH ADDITIVE WHITE AND ROUGH NOISES.SIAM JOURNAL ON NUMERICAL ANALYSIS,55(4),1958-1981.
MLA Cao, Yanzhao,et al."APPROXIMATING STOCHASTIC EVOLUTION EQUATIONS WITH ADDITIVE WHITE AND ROUGH NOISES".SIAM JOURNAL ON NUMERICAL ANALYSIS 55.4(2017):1958-1981.
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