NUMERICAL METHODS FOR FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

被引：79

作者：

Douglas, Jim, Jr. ^{[1
]}

Ma, Jin ^{[1
]}

Protter, Philip ^{[1
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

ANNALS OF APPLIED PROBABILITY | 1996年 / 6卷 / 03期

关键词：

Forward-backward stochastic differential equations; quasilinear parabolic equations; combined characteristics and finite difference method; Euler's scheme; weak convergence;

D O I：

10.1214/aoap/1034968235

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we study numerical methods to approximate the adapted solutions to a class of forward-backward stochastic differential equations (FBSDE's). The almost sure uniform convergence as well as the weak convergence of the scheme are proved, and the rate of convergence is proved to be as good as the approximation for the corresponding forward SDE. The idea of the approximation is based on the four step scheme for solving such an FBSDE, developed by Ma, Protter and Yong. For the PDE part, the combined characteristics and finite difference method is used, while for the forward SDE part, we use the first order Euler scheme.

引用

页码：940 / 968

页数：29

共 12 条

[1]

[Anonymous], ANN APPL PROBAB

[2]

Cvitanic J, 1996, ANN APPL PROBAB, V6, P370

[3]

Davis P., 1975, Interpolation Approximation

[4] FINITE-DIFFERENCE METHODS FOR 2-PHASE INCOMPRESSIBLE-FLOW IN POROUS-MEDIA [J].