A forward--backward stochastic algorithm for quasi-linear PDEs

Details A forward--backward stochastic algorithm for quasi-linear PDEs A forward--backward stochastic algorithm for quasi-linear PDEs

2006-03-10

arxiv.org/abs/math/0603250v1

Annals of Applied Probability 2006, Vol. 16, No. 1, 140-184

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000674 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000674

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.

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