Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

A Forward-Backward stochastic algorithm for quasi-linear PDEs


Code(s) de Classification MSC:

Résumé: 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

Date: 2004-09-10

Prépublication numéro: PMA-932