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2008 Quadratic BSDEs with Random Terminal Time and Elliptic PDEs in Infinite Dimension
Fulvia Confortola, Philippe Briand
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Electron. J. Probab. 13: 1529-1561 (2008). DOI: 10.1214/EJP.v13-514


In this paper we study one dimensional backward stochastic differential equations (BSDEs) with random terminal time not necessarily bounded or finite when the generator $F(t,Y,Z)$ has a quadratic growth in $Z$. We provide existence and uniqueness of a bounded solution of such BSDEs and, in the case of infinite horizon, regular dependence on parameters. The obtained results are then applied to prove existence and uniqueness of a mild solution to elliptic partial differential equations in Hilbert spaces. Finally we show an application to a control problem.


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Fulvia Confortola. Philippe Briand. "Quadratic BSDEs with Random Terminal Time and Elliptic PDEs in Infinite Dimension." Electron. J. Probab. 13 1529 - 1561, 2008.


Accepted: 17 September 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60071
MathSciNet: MR2438815
Digital Object Identifier: 10.1214/EJP.v13-514

Primary: 60H10
Secondary: 60H30

Keywords: elliptic PDEs , optimal stochastic control , Quadratic BSDEs

Vol.13 • 2008
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