The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 6, Number 3 (1996), 940-968.
Numerical methods for forward-backward stochastic differential equations
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.
Ann. Appl. Probab., Volume 6, Number 3 (1996), 940-968.
First available in Project Euclid: 18 October 2002
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Douglas, Jim; Ma, Jin; Protter, Philip. Numerical methods for forward-backward stochastic differential equations. Ann. Appl. Probab. 6 (1996), no. 3, 940--968. doi:10.1214/aoap/1034968235. https://projecteuclid.org/euclid.aoap/1034968235