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Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations
Yang, Jie1; Zhao, Weidong2,3; Zhou, Tao4
2019-06-01
Source PublicationJOURNAL OF SCIENTIFIC COMPUTING
ISSN0885-7474
Volume79Issue:3Pages:1409-1432
AbstractThis is the second part of our series papers on the deferred correction method for forward backward stochastic differential equations. In this work, we extend our previous work in Tang et al. (Numer Math Theory Methods Appl 10(2):222-242, 2017) to solve second-order forward backward stochastic differential equations (2FBSDEs). More precisely, we propose a class of explicit deferred correction schemes for 2FBSDEs. The key feature is that the simple Euler scheme is used as an initialization. Then, by a simple deferred correction iteration scheme, one can obtain an approximated solution with very high accuracy. Yet in each iteration, the computational complexity is always comparable to the Euler solver. Numerical examples are presented to show the effectiveness of the proposed scheme. We believe that the scheme proposed in this work is promising when dealing with 2FBSDEs in moderate dimensions.
KeywordDeferred correction method Second-order forward backward stochastic differential equations Euler scheme High-order rate of convergence
DOI10.1007/s10915-018-00896-w
Language英语
Funding Projectscience challenge Project[TZ2018001] ; NSF of China[11822111] ; NSF of China[11688101] ; NSF of China[91630203] ; NSF of China[11571351] ; NSF of China[11731006] ; NSF of China[11571206] ; NSF of China[11801320] ; national key basic research program[2018YFB0704304] ; NCMIS ; youth innovation promotion association (CAS) ; NSF of Shandong Province[ZR2018BA005]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000466934400003
PublisherSPRINGER/PLENUM PUBLISHERS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34839
Collection计算数学与科学工程计算研究所
Corresponding AuthorZhao, Weidong
Affiliation1.Shandong Univ, Sch Math & Stat, Weihai 264209, Shandong, 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
Recommended Citation
GB/T 7714
Yang, Jie,Zhao, Weidong,Zhou, Tao. Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations[J]. JOURNAL OF SCIENTIFIC COMPUTING,2019,79(3):1409-1432.
APA Yang, Jie,Zhao, Weidong,&Zhou, Tao.(2019).Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations.JOURNAL OF SCIENTIFIC COMPUTING,79(3),1409-1432.
MLA Yang, Jie,et al."Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations".JOURNAL OF SCIENTIFIC COMPUTING 79.3(2019):1409-1432.
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