A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis
文献类型：期刊论文
| 作者 | Flandoli, Franco4; Luo, Dejun2,3 ; Ricci, Cristiano1
|
| 刊名 | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
 |
| 出版日期 | 2021 |
| 卷号 | 493期号:1页码:29 |
| 关键词 | Kolmogorov equation Numerical solution Iteration schema Gaussian process |
| ISSN号 | 0022-247X |
| DOI | 10.1016/j.jmaa.2020.124505 |
| 英文摘要 | For Kolmogorov equations associated to finite dimensional stochastic differential equations (SDEs) in high dimension, a numerical method alternative to Monte Carlo simulations is proposed. The structure of the SDE is inspired by stochastic Partial Differential Equations (SPDE) and thus contains an underlying Gaussian process which is the key of the algorithm. A series development of the solution in terms of iterated integrals of the Gaussian process is given, it is proved to converge also in the infinite dimensional limit and it is numerically tested in a number of examples. (c) 2020 Elsevier Inc. All rights reserved. |
| 资助项目 | Scuola Normale Superiore[SNS19_B_FLANDOLI] ; Center for Climate Change Sustainable Action (3CSA) ; Scuola Normale Superiore di Pisa[SNS19_B_FLANDOLI] ; National Natural Science Foundation of China[11688101] ; Youth Innovation Promotion Association, CAS[2017003] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000576820100028 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/52334]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Flandoli, Franco |
| 作者单位 | 1.Univ Florence, Florence, Italy 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab RCSDS, Beijing 100190, Peoples R China 4.Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy |
| 推荐引用方式 GB/T 7714 | Flandoli, Franco,Luo, Dejun,Ricci, Cristiano. A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2021,493(1):29. |
| APA | Flandoli, Franco,Luo, Dejun,&Ricci, Cristiano.(2021).A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,493(1),29. |
| MLA | Flandoli, Franco,et al."A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 493.1(2021):29. |
入库方式： OAI收割
来源：数学与系统科学研究院
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