Backward stochastic differential equations and partial differential equations with quadratic growth
Magdalena Kobylanski
Source: Ann. Probab. Volume 28, Number 2
(2000), 558-602.
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.
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Keywords: Backward stochastic differential equations; comparison principle; semilinear partial differential equations; viscosity solutions; Feynman–Kac formula
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1019160253
Mathematical Reviews number (MathSciNet): MR1782267
Digital Object Identifier: doi:10.1214/aop/1019160253
Zentralblatt MATH identifier: 01906369
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