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

   
@article{EJP514,
	author = {Fulvia Confortola and Philippe Briand},
	title = {Quadratic BSDEs with Random Terminal Time and Elliptic PDEs in Infinite Dimension},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {13},
	year = {2008},
	keywords = {Quadratic BSDEs; elliptic PDEs; optimal stochastic control},
	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.},
	pages = {no. 54, 1529-1561},
	issn = {1083-6489},
	doi = {10.1214/EJP.v13-514},    
        url = {http://ejp.ejpecp.org/article/view/514}}