A Forward-Backward stochastic algorithm for quasi-linear PDEs
Delarue, François ; Menozzi, Séphane
HAL, hal-00002980 / Harvested from HAL
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.
Publié le : 2004-09-30
Classification:  Quasi-linear PDEs,  Quantization,  FBSDEs,  Discretization scheme,  65C30, 35K55, 60H10, 60H35.,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00002980,
     author = {Delarue, Fran\c cois and Menozzi, S\'ephane},
     title = {A Forward-Backward stochastic algorithm for quasi-linear PDEs},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00002980}
}
Delarue, François; Menozzi, Séphane. A Forward-Backward stochastic algorithm for quasi-linear PDEs. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00002980/