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August 1996 Numerical methods for forward-backward stochastic differential equations
Jim Douglas Jr., Jin Ma, Philip Protter
Ann. Appl. Probab. 6(3): 940-968 (August 1996). DOI: 10.1214/aoap/1034968235

Abstract

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.

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Jim Douglas Jr.. Jin Ma. Philip Protter. "Numerical methods for forward-backward stochastic differential equations." Ann. Appl. Probab. 6 (3) 940 - 968, August 1996. https://doi.org/10.1214/aoap/1034968235

Information

Published: August 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0861.65131
MathSciNet: MR1410123
Digital Object Identifier: 10.1214/aoap/1034968235

Subjects:
Primary: 65U05
Secondary: 60H10 , 65M06 , 65M25

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

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 3 • August 1996
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