A forward--backward stochastic algorithm for quasi-linear PDEs
Abstract
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 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--968] and weakens the regularity assumptions required in this reference.
Keywords
Cite
@article{arxiv.math/0603250,
title = {A forward--backward stochastic algorithm for quasi-linear PDEs},
author = {François Delarue and Stéphane Menozzi},
journal= {arXiv preprint arXiv:math/0603250},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/105051605000000674 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)