A Forward-Backward stochastic algorithm for quasi-linear PDEsReport as inadecuate

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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 CMAP - Centre de Mathématiques Appliquées

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 equations. 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 DMP96 and weakens the regularity assumptions required in this reference.

keyword : Quasi-linear PDEs Quantization FBSDEs Discretization scheme

Author: François Delarue - Séphane Menozzi -

Source: https://hal.archives-ouvertes.fr/


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