BSDE on an infinite horizon and elliptic PDEs in infinite dimension

Ying Hu (1) , Gianmario Tessitore (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Dipartimento di Matematica e Applicazioni [Milano]

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

Mots clés: Backward Stochastic differential equations Elliptic PDEs; Hilbert spaces; Mild Solutions

Domaines: Probabilités [math.PR]

Ying Hu, Gianmario Tessitore. BSDE on an infinite horizon and elliptic PDEs in infinite dimension. Nonlinear Differential Equations and Applications, 2007, 14 (5-6), pp.825-846. ⟨10.1007/s00030-007-6029-5⟩. ⟨hal-00368765⟩