The Annals of Probability
- Ann. Probab.
- Volume 28, Number 2 (2000), 558-602.
Backward stochastic differential equations and partial differential equations with quadratic growth
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.
Ann. Probab. Volume 28, Number 2 (2000), 558-602.
First available in Project Euclid: 18 April 2002
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Kobylanski, Magdalena. Backward stochastic differential equations and partial differential equations with quadratic growth. Ann. Probab. 28 (2000), no. 2, 558--602. doi:10.1214/aop/1019160253. https://projecteuclid.org/euclid.aop/1019160253