Displaying similar documents to “On a class of forward-backward stochastic differential systems in infinite dimensions.”

Optimal control of a stochastic heat equation with boundary-noise and boundary-control

Arnaud Debussche, Marco Fuhrman, Gianmario Tessitore (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We are concerned with the optimal control of a nonlinear stochastic heat equation on a bounded real interval with Neumann boundary conditions. The specificity here is that both the control and the noise act on the boundary. We start by reformulating the state equation as an infinite dimensional stochastic evolution equation. The first main result of the paper is the proof of existence and uniqueness of a mild solution for the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The...

SPDEs with coloured noise: Analytic and stochastic approaches

Marco Ferrante, Marta Sanz-Solé (2006)

ESAIM: Probability and Statistics

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We study strictly parabolic stochastic partial differential equations on ℝ d , ≥ 1, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give sufficient conditions on the correlation of the noise ensuring Hölder continuity for the trajectories of the solution of the equation. For self-adjoint operators with deterministic coefficients, the mild and weak formulation of the equation are...