Marín-Rubio, Pedro; Real, José Probabilistic representation of solutions for quasi-linear parabolic PDE via FBSDE with reflecting boundary conditions. (English) Zbl 1242.60055 Bol. Soc. Esp. Mat. Apl., S\(\vec{\text{e}}\)MA 51, 109-116 (2010). Summary: A probabilistic representation of the solution (in the viscosity sense) of a quasi-linear parabolic PDE system with non-Lipschitz terms and Neumann boundary conditions is given via a fully coupled forward-backward stochastic differential equation with a reflecting term in the forward equation. The extension of previous results consists of the relaxation of the Lipschitz assumption on the drift coefficient of the forward equation, using a previous result of the authors. MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 35R60 PDEs with randomness, stochastic partial differential equations 60J60 Diffusion processes PDFBibTeX XMLCite \textit{P. Marín-Rubio} and \textit{J. Real}, Bol. Soc. Esp. Mat. Apl., S\(\vec{\text{e}}\)MA 51, 109--116 (2010; Zbl 1242.60055) Full Text: DOI