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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 54 open journal systems 


Quadratic BSDEs with random terminal time and elliptic PDEs in infinite dimension.

Fulvia Confortola, Politecnico di Milano
Philippe Briand, IRMAR, Université Rennes 1


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.


Full text: PDF

Pages: 1529-1561

Published on: September 17, 2008
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Electronic Journal of Probability. ISSN: 1083-6489