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


 
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1. Title Title of document Quadratic BSDEs with Random Terminal Time and Elliptic PDEs in Infinite Dimension
 
2. Creator Author's name, affiliation, country Fulvia Confortola; Politecnico di Milano
 
2. Creator Author's name, affiliation, country Philippe Briand; IRMAR, Université Rennes 1
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Quadratic BSDEs; elliptic PDEs; optimal stochastic control
 
3. Subject Subject classification 60H10;60H30
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2008-09-17
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/514
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-514
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
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