The Annals of Probability

Backward stochastic differential equations and partial differential equations with quadratic growth

Magdalena Kobylanski

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Abstract

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

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

Dates
First available in Project Euclid: 18 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1019160253

Digital Object Identifier
doi:10.1214/aop/1019160253

Mathematical Reviews number (MathSciNet)
MR1782267

Zentralblatt MATH identifier
1044.60045

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

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

Citation

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


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