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February 2006 A forward–backward stochastic algorithm for quasi-linear PDEs
François Delarue, Stéphane Menozzi
Ann. Appl. Probab. 16(1): 140-184 (February 2006). DOI: 10.1214/105051605000000674


We propose a time-space discretization scheme for quasi-linear parabolic PDEs. The algorithm relies on the theory of fully coupled forward–backward SDEs, which provides an efficient probabilistic representation of this type of equation. The derivated algorithm holds for strong solutions defined on any interval of arbitrary length. As a bypass product, we obtain a discretization procedure for the underlying FBSDE. In particular, our work provides an alternative to the method described in [Douglas, Ma and Protter (1996) Ann. Appl. Probab. 6 940–968] and weakens the regularity assumptions required in this reference.


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François Delarue. Stéphane Menozzi. "A forward–backward stochastic algorithm for quasi-linear PDEs." Ann. Appl. Probab. 16 (1) 140 - 184, February 2006.


Published: February 2006
First available in Project Euclid: 6 March 2006

zbMATH: 1097.65011
MathSciNet: MR2209339
Digital Object Identifier: 10.1214/105051605000000674

Primary: 65C30
Secondary: 35K55, 60H10, 60H35

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.16 • No. 1 • February 2006
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