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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（5）
• 页码范围: 923-948
• 页数: 26页
• 语种: 英文
• DOI: 10.1007/s11425-016-0178-8

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 Ito-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.