@article {50, title = {A forward{\textendash}backward stochastic algorithm for quasi-linear PDEs}, journal = {Annals of Applied Probability}, volume = {16(1)}, year = {2006}, pages = {140-184}, abstract = {We propose a time-space discretization scheme for quasi-linear parabolic PDEs. The algorithm relies on the theory of fully coupled forward{\textendash}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{\textendash}968] and weakens the regularity assumptions required in this reference. }, author = {Fran{\c c}ois Delarue and St{\'e}phane Menozzi} }