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.

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Pages: 1529-1561

Publication Date: September 17, 2008

DOI: 10.1214/EJP.v13-514

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