APPROXIMATING STOCHASTIC EVOLUTION EQUATIONS WITH ADDITIVE WHITE AND ROUGH NOISES

doi:10.1137/16M1056122

	APPROXIMATING STOCHASTIC EVOLUTION EQUATIONS WITH ADDITIVE WHITE AND ROUGH NOISES
	Cao, Yanzhao 1,2; Hong, Jialin3 ; Liu, Zhihui 3
	2017
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	55 期号:4 页码:1958-1981
摘要	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.
关键词	stochastic evolution equation fractional Brownian motion Wong-Zakai approximation Galerkin approximation
DOI	10.1137/16M1056122
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000408925300017
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/26458
专题	计算数学与科学工程计算研究所
通讯作者	Liu, Zhihui
作者单位	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
推荐引用方式 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.