The Annals of Probability

Backward stochastic differential equations and partial differential equations with quadratic growth

Magdalena Kobylanski

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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.

Article information

Ann. Probab. Volume 28, Number 2 (2000), 558-602.

First available in Project Euclid: 18 April 2002

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Zentralblatt MATH identifier

Primary: 60H20: Stochastic integral equations 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 35J60: Nonlinear elliptic equations 35k55

Backward stochastic differential equations comparison principle semilinear partial differential equations viscosity solutions Feynman–Kac formula


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.

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