A forward-backward stochastic algorithm for quasi-linear PDEs

DOI10.1214/105051605000000674zbMATH Open1097.65011arXivmath/0603250OpenAlexW2164907988MaRDI QIDQ2494576

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Publication date: 29 June 2006

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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.

Full work available at URL: https://arxiv.org/abs/math/0603250

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