Annals of Applied Probability

A forward–backward stochastic algorithm for quasi-linear PDEs

François Delarue and Stéphane Menozzi

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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.

Article information

Ann. Appl. Probab., Volume 16, Number 1 (2006), 140-184.

First available in Project Euclid: 6 March 2006

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Zentralblatt MATH identifier

Primary: 65C30: Stochastic differential and integral equations
Secondary: 35K55: Nonlinear parabolic equations 60H10: Stochastic ordinary differential equations [See also 34F05] 60H35: Computational methods for stochastic equations [See also 65C30]

Discretization scheme FBSDEs quantization quasi-linear PDEs


Delarue, François; Menozzi, Stéphane. A forward–backward stochastic algorithm for quasi-linear PDEs. Ann. Appl. Probab. 16 (2006), no. 1, 140--184. doi:10.1214/105051605000000674.

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