Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density
文献类型：期刊论文
| 作者 | Chen, Chuchu2,3; Cui, Jianbo1; Hong, Jialin2,3; Sheng, Derui2,3 |
| 刊名 | IMA JOURNAL OF NUMERICAL ANALYSIS
 |
| 出版日期 | 2022-04-19 |
| 页码 | 40 |
| 关键词 | density convergence order accelerated exponential Euler scheme stochastic heat equation Malliavin calculus |
| ISSN号 | 0272-4979 |
| DOI | 10.1093/imanum/drac011 |
| 英文摘要 | 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. |
| 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 ; Hong Kong Polytechnic University[P0039016] ; CAS AMSS-PolyU Joint Laboratory of Applied Mathematics |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000786107500001 |
| 出版者 | OXFORD UNIV PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60319]  |
| 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.Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Kowloon, Hong Kong 999077, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。