A Forward-Backward stochastic algorithm for quasi-linear PDEs

François Delarue (1) , Séphane Menozzi (1, 2)

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

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.

Mots clés: Discretization scheme; FBSDEs; Quantization; Quasi-linear PDEs

Domaines: Probabilités [math.PR]

François Delarue, Séphane Menozzi. A Forward-Backward stochastic algorithm for quasi-linear PDEs. 2004. ⟨hal-00002980⟩