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A forward--backward stochastic algorithm for quasi-linear PDEs

François Delarue·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.

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François Delarue, Stéphane Menozzi. 2006-03-10. A forward--backward stochastic algorithm for quasi-linear PDEs. https://doi.org/10.1214/105051605000000674

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