Electronic Journal of Probability

Quadratic BSDEs with Random Terminal Time and Elliptic PDEs in Infinite Dimension

Fulvia Confortola and Philippe Briand

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Abstract

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.

Article information

Source
Electron. J. Probab., Volume 13 (2008), paper no. 54, 1529-1561.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819127

Digital Object Identifier
doi:10.1214/EJP.v13-514

Mathematical Reviews number (MathSciNet)
MR2438815

Zentralblatt MATH identifier
1191.60071

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Quadratic BSDEs elliptic PDEs optimal stochastic control

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Confortola, Fulvia; Briand, Philippe. Quadratic BSDEs with Random Terminal Time and Elliptic PDEs in Infinite Dimension. Electron. J. Probab. 13 (2008), paper no. 54, 1529--1561. doi:10.1214/EJP.v13-514. https://projecteuclid.org/euclid.ejp/1464819127


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