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.e 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.
Primary Subjects: 60H20, 60H30
Secondary Subjects: 35J60, 35k55
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