×

Probabilistic representation of solutions for quasi-linear parabolic PDE via FBSDE with reflecting boundary conditions. (English) Zbl 1242.60055

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
Full Text: DOI