Influence of numerical discretizations on hitting probabilities for linear stochastic parabolic systems

doi:10.1016/j.jco.2021.101634

	Influence of numerical discretizations on hitting probabilities for linear stochastic parabolic systems
	Chen, Chuchu 1,2; Hong, Jialin 1,2; Sheng, Derui 1,2
刊名	JOURNAL OF COMPLEXITY
	2022-06-01
卷号	70 页码:29
关键词	Hitting probability Numerical discretization Stochastic parabolic system Critical dimension
ISSN号	0885-064X
DOI	10.1016/j.jco.2021.101634
英文摘要	This paper investigates the influence of standard numerical discretizations on hitting probabilities for a system of linear stochastic parabolic equations driven by space-time white noises. We establish lower and upper bounds for hitting probabilities of the associated numerical solutions of both temporal and spatial semi-discretizations in terms of Bessel-Riesz capacity and Hausdorff measure, respectively. Moreover, the critical dimensions of both temporal and spatial semi-discretizations turn out to be halves of those of the exact solution. This reveals that there exist some Borel sets Asuch that the probability of the event that the paths of the numerical solution hit Acannot converge to that of the exact solution when the stepsizes vanish. (C) 2021 Elsevier Inc. All rights reserved.
资助项目	National Natural Science Foundation of China[11971470] ; National Natural Science Foundation of China[11871068] ; National Natural Science Foundation of China[12031020] ; National Natural Science Foundation of China[12022118] ; Youth Innovation Promotion Association CAS
WOS研究方向	Computer Science ; Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000766626700006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60145]
专题	中国科学院数学与系统科学研究院
通讯作者	Sheng, Derui
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Chen, Chuchu,Hong, Jialin,Sheng, Derui. Influence of numerical discretizations on hitting probabilities for linear stochastic parabolic systems[J]. JOURNAL OF COMPLEXITY,2022,70:29.
APA	Chen, Chuchu,Hong, Jialin,&Sheng, Derui.(2022).Influence of numerical discretizations on hitting probabilities for linear stochastic parabolic systems.JOURNAL OF COMPLEXITY,70,29.
MLA	Chen, Chuchu,et al."Influence of numerical discretizations on hitting probabilities for linear stochastic parabolic systems".JOURNAL OF COMPLEXITY 70(2022):29.