A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis

doi:10.1016/j.jmaa.2020.124505

CSpace > 应用数学研究所

	A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis
	Flandoli, Franco 1; Luo, Dejun2,3 ; Ricci, Cristiano 4
	2021
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	493 期号:1 页码:29
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.
关键词	Kolmogorov equation Numerical solution Iteration schema Gaussian process
DOI	10.1016/j.jmaa.2020.124505
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000576820100028
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52335
专题	应用数学研究所
通讯作者	Flandoli, Franco
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 Florence, Florence, 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.