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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.

MSC:
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.)
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