Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation br
文献类型：期刊论文
| 作者 | Flandoli, Franco1; Luo, Dejun3,4 ; Ricci, Cristiano2
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| 刊名 | APPLIED MATHEMATICS AND COMPUTATION
 |
| 出版日期 | 2023 |
| 卷号 | 436页码:17 |
| 关键词 | High dimensional Kolmogorov equation Numerical solution Iteration scheme Gaussian process |
| ISSN号 | 0096-3003 |
| DOI | 10.1016/j.amc.2022.127520 |
| 英文摘要 | Stochastic Differential Equations (SDEs) in high dimension, having the structure of finite dimensional approximation of Stochastic Partial Differential Equations (SPDEs), are consid-ered. The aim is to numerically compute the expected values and probabilities associated to their solutions, by solving the corresponding Kolmogorov equations, with a partial use of Monte Carlo strategy -precisely, using Monte Carlo only for the linear part of the SDE. The basic idea was presented in [16], but here we strongly improve the numerical results by means of a shift of the auxiliary Gaussian process. For relatively simple nonlinearities, we have good results in dimension of the order of 100. (c) 2022 Elsevier Inc. All rights reserved. |
| 资助项目 | National Key R&D Program of China[2020YFA0712700] ; National Natural Science Foundation of China[11931004] ; National Natural Science Foundation of China[12090014] ; Youth Innovation Promotion Association, CAS[Y2021002] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000860361200003 |
| 出版者 | ELSEVIER SCIENCE INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60980]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Ricci, Cristiano |
| 作者单位 | 1.Scuola Normale Super Pisa, Piazza Cavalieri, 7, I-56126 Pisa, Italy 2.Univ Pisa, Lungarno Pacinotti 43, I-56126 Pisa, Italy 3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab RCSDS, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Flandoli, Franco,Luo, Dejun,Ricci, Cristiano. Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation br[J]. APPLIED MATHEMATICS AND COMPUTATION,2023,436:17. |
| APA | Flandoli, Franco,Luo, Dejun,&Ricci, Cristiano.(2023).Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation br.APPLIED MATHEMATICS AND COMPUTATION,436,17. |
| MLA | Flandoli, Franco,et al."Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation br".APPLIED MATHEMATICS AND COMPUTATION 436(2023):17. |
入库方式： OAI收割
来源：数学与系统科学研究院
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