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Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs

文献类型：期刊论文

作者Kong, Tao1,2; Zhao, Weidong1,2; Zhou, Tao3
刊名COMMUNICATIONS IN COMPUTATIONAL PHYSICS
出版日期2015-11-01
卷号18期号:5页码:1482-1503
关键词Fully nonlinear parabolic PDEs second order FBSDEs probabilistic interpretations probabilistic numerical schemes
ISSN号1815-2406
DOI10.4208/cicp.240515.280815a
英文摘要In this paper, we are concerned with probabilistic high order numerical schemes for Cauchy problems of fully nonlinear parabolic PDEs. For such parabolic PDEs, it is shown by Cheridito, Soner, Touzi and Victoir [4] that the associated exact solutions admit probabilistic interpretations, i.e., the solution of a fully nonlinear parabolic PDE solves a corresponding second order forward backward stochastic differential equation (2FBSDEs). Our numerical schemes rely on solving those 2FBSDEs, by extending our previous results [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci, Comput., 36 (2014), pp. A1731-A1751.]. Moreover, in our numerical schemes, one has the flexibility to choose the associated forward SDE, and a suitable choice can significantly reduce the computational complexity. Various numerical examples including the HJB equations are presented to show the effectiveness and accuracy of the proposed numerical schemes.
资助项目National Natural Science Foundations of China[91130003] ; National Natural Science Foundations of China[11201461] ; National Natural Science Foundations of China[11171189]
WOS研究方向Physics
语种英语
WOS记录号WOS:000365681400012
出版者GLOBAL SCIENCE PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/21408]  
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, Sch Math, Jinan 250100, Peoples R China
2.Shandong Univ, Finance Inst, Jinan 250100, Peoples R China
3.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		 Kong, Tao,Zhao, Weidong,Zhou, Tao. Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2015,18(5):1482-1503.
APA Kong, Tao,Zhao, Weidong,&Zhou, Tao.(2015).Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,18(5),1482-1503.
MLA Kong, Tao,et al."Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 18.5(2015):1482-1503.

入库方式： OAI收割

来源：数学与系统科学研究院

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