A UNIFIED PROBABILISTIC DISCRETIZATION SCHEME FOR FBSDEs: STABILITY, CONSISTENCY, AND CONVERGENCE ANALYSIS

doi:10.1137/19M1260177

	A UNIFIED PROBABILISTIC DISCRETIZATION SCHEME FOR FBSDEs: STABILITY, CONSISTENCY, AND CONVERGENCE ANALYSIS
	Yang, Jie 5; Zhao, Weidong 3,4; Zhou, Tao 1,2
刊名	SIAM JOURNAL ON NUMERICAL ANALYSIS
	2020
卷号	58 期号:4 页码:2351-2375
关键词	forward backward stochastic differential equations numerical schemes stability consistency convergence analysis
ISSN号	0036-1429
DOI	10.1137/19M1260177
英文摘要	In this work, we propose a general discretization framework for numerical solution of forward backward stochastic differential equations (FBSDEs). The framework covers several existing temporal discretization probabilistic schemes in the literature. The consistency, stability, and convergence analysis for the proposed scheme are presented. In particular, we prove a stochastic mean square version of Lax equivalence theorem-showing that a consistent discretization scheme for FBSDEs is convergent if and only if it is stable. Applications of the analysis results to existing numerical schemes are also discussed.
资助项目	National Key Basic Research Program[2018YFB0704304] ; National Key Basic Research Program[2018YFA0703903] ; National Natural Science Foundation of China[11822111] ; National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[11731006] ; National Natural Science Foundation of China[11571206] ; National Natural Science Foundation of China[11831010] ; National Natural Science Foundation of China[11801320] ; Youth Innovation Promotion Association of CAS ; National Natural Science Foundation of Shandong Province[ZR2018BA005] ; Science Challenge Project[TZ2018001]
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000568220000015
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52148]
专题	中国科学院数学与系统科学研究院
通讯作者	Yang, Jie
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Beijing 100190, Peoples R China 3.Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China 4.Shandong Univ, Inst Finance, Jinan 250100, Shandong, Peoples R China 5.Shandong Univ, Sch Math & Stat, Weihai 264209, Shandong, Peoples R China
推荐引用方式 GB/T 7714	Yang, Jie,Zhao, Weidong,Zhou, Tao. A UNIFIED PROBABILISTIC DISCRETIZATION SCHEME FOR FBSDEs: STABILITY, CONSISTENCY, AND CONVERGENCE ANALYSIS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2020,58(4):2351-2375.
APA	Yang, Jie,Zhao, Weidong,&Zhou, Tao.(2020).A UNIFIED PROBABILISTIC DISCRETIZATION SCHEME FOR FBSDEs: STABILITY, CONSISTENCY, AND CONVERGENCE ANALYSIS.SIAM JOURNAL ON NUMERICAL ANALYSIS,58(4),2351-2375.
MLA	Yang, Jie,et al."A UNIFIED PROBABILISTIC DISCRETIZATION SCHEME FOR FBSDEs: STABILITY, CONSISTENCY, AND CONVERGENCE ANALYSIS".SIAM JOURNAL ON NUMERICAL ANALYSIS 58.4(2020):2351-2375.