Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation br

doi:10.1016/j.amc.2022.127520

CSpace > 应用数学研究所

	Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation br
	Flandoli, Franco 1; Luo, Dejun2,3 ; Ricci, Cristiano 4
	2023
发表期刊	APPLIED MATHEMATICS AND COMPUTATION
ISSN	0096-3003
卷号	436 页码:17
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.
关键词	High dimensional Kolmogorov equation Numerical solution Iteration scheme Gaussian process
DOI	10.1016/j.amc.2022.127520
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000860361200003
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60981
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.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab RCSDS, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Univ Pisa, Lungarno Pacinotti 43, I-56126 Pisa, Italy
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.