Convergence error estimates of the Crank-Nicolson scheme for solving decoupled FBSDEs  

作　　者：LI Yang YANG Jie ZHAO WeiDong 

机构地区：[1]College of Science,University of Shanghai for Science and Technology [2]School of Mathematics,Shandong University

出　　处：《Science China Mathematics》2017年第5期923-948,共26页中国科学：数学（英文版）

基　　金：supported by Shanghai University Young Teacher Training Program(Grant No.slg14032);National Natural Science Foundations of China(Grant Nos.11501366 and 11571206)

摘　　要：In this work, we theoretically analyze the convergence error estimates of the Crank-Nicolson （C-N） scheme for solving decoupled FBSDEs. Based on the Taylor and ItS-Taylor expansions, the Malliavin calculus theory （e.g., the multiple Malliavin integration-by-parts formula）, and our new truncation error cancelation techniques, we rigorously prove that the strong convergence rate of the C-N scheme is of second order for solving decoupled FBSDEs, which fills the gap between the second-order numerical and theoretical analysis of the C-N scheme.In this work, we theoretically analyze the convergence error estimates of the Crank-Nicolson(C-N) scheme for solving decoupled FBSDEs. Based on the Taylor and It-Taylor expansions, the Malliavin calculus theory(e.g.,the multiple Malliavin integration-by-parts formula), and our new truncation error cancelation techniques, we rigorously prove that the strong convergence rate of the C-N scheme is of second order for solving decoupled FBSDEs, which fills the gap between the second-order numerical and theoretical analysis of the C-N scheme.

关 键 词：convergence analysis Crank-Nicolson scheme decoupled forward backward stochastic differentialequations Malliavin calculus trapezoidal rule 

分 类 号：O211.63[理学—概率论与数理统计] O241.82[理学—数学]