System Modeling and Optimization

In this paper we study the stochastic maximum principle for a control problem in infinite dimensions. This problem is governed by a fully coupled forward-backward doubly stochastic differential equation (FBDSDE) driven by two cylindrical Wiener processes on separable Hilbert spaces and a Poisson random measure. We allow the control variable to enter in all coefficients appearing in this system. Existence anduniqueness of the solutions of FBDSDEs and an extended martingale representation theorem are provided as well.

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