Annals of Applied Probability

A forward–backward stochastic algorithm for quasi-linear PDEs

François Delarue and Stéphane Menozzi

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Abstract

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

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

Dates
First available in Project Euclid: 6 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1141654284

Digital Object Identifier
doi:10.1214/105051605000000674

Mathematical Reviews number (MathSciNet)
MR2209339

Zentralblatt MATH identifier
1097.65011

Subjects
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]

Keywords
Discretization scheme FBSDEs quantization quasi-linear PDEs

Citation

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. https://projecteuclid.org/euclid.aoap/1141654284


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Annals of Applied Probability

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