CSpace
Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density
Chen, Chuchu1,2; Cui, Jianbo3; Hong, Jialin1,2; Sheng, Derui1,2
2022-04-19
Source PublicationIMA JOURNAL OF NUMERICAL ANALYSIS
ISSN0272-4979
Pages40
AbstractThis paper studies the numerical approximation of the density of the stochastic heat equation driven by space-time white noise via the accelerated exponential Euler scheme. The existence and smoothness of the density of the numerical solution are proved by means of Malliavin calculus. Based on a priori estimates of the numerical solution we present a test-function-independent weak convergence analysis, which is crucial to show the convergence of the density. The convergence order of the density in uniform convergence topology is shown to be exactly 1/2 in the nonlinear drift case and nearly 1 in the affine drift case. As far as we know, this is the first result on the existence and convergence of density of the numerical solution to the stochastic partial differential equation.
Keyworddensity convergence order accelerated exponential Euler scheme stochastic heat equation Malliavin calculus
DOI10.1093/imanum/drac011
Indexed BySCI
Language英语
Funding ProjectNational 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 ; Hong Kong Polytechnic University[P0039016] ; CAS AMSS-PolyU Joint Laboratory of Applied Mathematics
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000786107500001
PublisherOXFORD UNIV PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/60320
Collection中国科学院数学与系统科学研究院
Corresponding AuthorSheng, Derui
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Kowloon, Hong Kong 999077, Peoples R China
Recommended Citation
GB/T 7714
Chen, Chuchu,Cui, Jianbo,Hong, Jialin,et al. Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2022:40.
APA Chen, Chuchu,Cui, Jianbo,Hong, Jialin,&Sheng, Derui.(2022).Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density.IMA JOURNAL OF NUMERICAL ANALYSIS,40.
MLA Chen, Chuchu,et al."Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density".IMA JOURNAL OF NUMERICAL ANALYSIS (2022):40.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Chen, Chuchu]'s Articles
[Cui, Jianbo]'s Articles
[Hong, Jialin]'s Articles
Baidu academic
Similar articles in Baidu academic
[Chen, Chuchu]'s Articles
[Cui, Jianbo]'s Articles
[Hong, Jialin]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Chen, Chuchu]'s Articles
[Cui, Jianbo]'s Articles
[Hong, Jialin]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.