KMS Of Academy of mathematics and systems sciences, CAS
| APPROXIMATING STOCHASTIC EVOLUTION EQUATIONS WITH ADDITIVE WHITE AND ROUGH NOISES | |
Cao, Yanzhao1,2; Hong, Jialin3 ; Liu, Zhihui3
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| 2017 | |
| Source Publication | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| ISSN | 0036-1429 |
| Volume | 55Issue:4Pages:1958-1981 |
| Abstract | In 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. |
| Keyword | stochastic evolution equation fractional Brownian motion Wong-Zakai approximation Galerkin approximation |
| DOI | 10.1137/16M1056122 |
| Language | 英语 |
| Funding Project | National 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 Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000408925300017 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/26458 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Liu, Zhihui |
| Affiliation | 1.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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