A forward–backward stochastic algorithm for quasi-linear PDEs

Abstract

We propose a time-space discretization scheme for quasi-linear parabolic\nPDEs. The algorithm relies on the theory of fully coupled forward--backward\nSDEs, which provides an efficient probabilistic representation of this type of\nequation. The derivated algorithm holds for strong solutions defined on any\ninterval of arbitrary length. As a bypass product, we obtain a discretization\nprocedure for the underlying FBSDE. In particular, our work provides an\nalternative to the method described in [Douglas, Ma and Protter (1996) Ann.\nAppl. Probab. 6 940--968] and weakens the regularity assumptions required in\nthis reference.\n