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Backward stochastic differential equations and partial differential equations with quadratic growth. (English) Zbl 1044.60045
Summary: We provide existence, comparison and stability results for one-dimensional backward stochastic differential equations (BSDEs) when the coefficient (or generator) \(F(t,Y,Z)\) is continuous and has a quadratic growth in \(Z\) and the terminal condition is bounded. We also give, in this framework, the links between the solutions of BSDEs set on a diffusion and viscosity or Sobolev solutions of the corresponding semilinear partial differential equations.

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
Full Text: DOI
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