KMS Of Academy of mathematics and systems sciences, CAS
| 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 Publication | IMA JOURNAL OF NUMERICAL ANALYSIS
 |
| ISSN | 0272-4979 |
| Pages | 40 |
| Abstract | This 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. |
| Keyword | density convergence order accelerated exponential Euler scheme stochastic heat equation Malliavin calculus |
| DOI | 10.1093/imanum/drac011 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 ; Hong Kong Polytechnic University[P0039016] ; CAS AMSS-PolyU Joint Laboratory of Applied Mathematics |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000786107500001 |
| Publisher | OXFORD UNIV PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60320 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Sheng, Derui |
| Affiliation | 1.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. |
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