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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