Stochastic Maximum Principle for Hilbert Space Valued Forward-Backward Doubly SDEs with Poisson Jumps

Abstract : 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 and uniqueness of the solutions of FBDSDEs and an extended martingale representation theorem are provided as well.
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Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.1-10, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_1〉
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Abdulrahman Al-Hussein, Boulakhras Gherbal. Stochastic Maximum Principle for Hilbert Space Valued Forward-Backward Doubly SDEs with Poisson Jumps. Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.1-10, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_1〉. 〈hal-01286214〉

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