BSDE on an infinite horizon and elliptic PDEs in infinite dimension |
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Authors: | Ying Hu Gianmario Tessitore |
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Institution: | (1) IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France;(2) Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via R. Cozzi 53 - Edificio U5, 20125 Milano, Italy |
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Abstract: | In this paper, we study the existence and uniqueness of mild solutions to a possibly degenerate elliptic partial differential
equation in Hilbert spaces. Our aim is, in the case in which ψ(·, 0, 0) is bounded, to drop the assumptions on the size of λ needed in 11]. The main tool will be existence, uniqueness
and regular dependence on parameters of a bounded solution to a suitable backward stochastic differential equation with infinite
horizon. Finally we apply the result to study an optimal control problem.
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Keywords: | 60H10 |
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