EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES

doi:10.3934/dedsb.2017174

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES
	Fu, Yu 1,2,3; Zhao, Weidong 2,3; Zhou, Tao4
刊名	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
	2017-11-01
卷号	22 期号:9 页码:3439-3458
关键词	Spectral method sparse grid approximations forward backward stochastic differential equations conditional expectations fast Fourier transform
ISSN号	1531-3492
DOI	10.3934/dedsb.2017174
英文摘要	This is the second part of a series papers on multi-step schemes for solving coupled forward backward stochastic differential equations (FBSDEs). We extend the basic idea in our former paper [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751] to solve high-dimensional FBSDEs, by using the spectral sparse grid approximations. The main issue for solving high-dimensional FBSDEs is to build an efficient spatial discretization, and deal with the related high-dimensional conditional expectations and interpolations. In this work, we propose the sparse grid spatial discretization. The sparse grid Gaussian-Hermite quadrature rule is used to approximate the conditional expectations. And for the associated high-dimensional interpolations, we adopt a spectral expansion of functions in polynomial spaces with respect to the spatial variables, and use the sparse grid approximations to recover the expansion coefficients. The FFT algorithm is used to speed up the recovery procedure, and the entire algorithm admits efficient and highly accurate approximations in high dimensions. Several numerical examples are presented to demonstrate the efficiency of the proposed methods.
资助项目	National Natural Science Foundations of China[91630312] ; National Natural Science Foundations of China[91630203] ; National Natural Science Foundations of China[11571351] ; National Natural Science Foundations of China[11171189] ; National Natural Science Foundations of China[11571206] ; NCMIS
WOS研究方向	Mathematics
语种	英语
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
WOS记录号	WOS:000409963100011
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/26565]
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Tao
作者单位	1.Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China 2.Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China 3.Shandong Univ, Inst Finance, Jinan 250100, Shandong, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Fu, Yu,Zhao, Weidong,Zhou, Tao. EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2017,22(9):3439-3458.
APA	Fu, Yu,Zhao, Weidong,&Zhou, Tao.(2017).EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,22(9),3439-3458.
MLA	Fu, Yu,et al."EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 22.9(2017):3439-3458.