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April 2000 Backward stochastic differential equations and partial differential equations with quadratic growth
Magdalena Kobylanski
Ann. Probab. 28(2): 558-602 (April 2000). DOI: 10.1214/aop/1019160253

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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Magdalena Kobylanski. "Backward stochastic differential equations and partial differential equations with quadratic growth." Ann. Probab. 28 (2) 558 - 602, April 2000. https://doi.org/10.1214/aop/1019160253

Information

Published: April 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60045
MathSciNet: MR1782267
Digital Object Identifier: 10.1214/aop/1019160253

Subjects:
Primary: 60H20 , 60H30
Secondary: 35J60 , 35K55

Keywords: Backward stochastic differential equations , Comparison principle , Feynman–Kac formula , semilinear partial differential equations , viscosity solutions

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 2 • April 2000
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