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Necessary Conditions for Optimal Control of Stochastic Evolution Equations in Hilbert Spaces

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Abstract

We consider a nonlinear stochastic optimal control problem associated with a stochastic evolution equation. This equation is driven by a continuous martingale in a separable Hilbert space and an unbounded time-dependent linear operator.

We derive a stochastic maximum principle for this optimal control problem. Our results are achieved by using the adjoint backward stochastic partial differential equation.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah, 51452, Saudi Arabia

    AbdulRahman Al-Hussein

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  1. AbdulRahman Al-Hussein
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Correspondence to AbdulRahman Al-Hussein.

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Communicating Editor: Alain Bensoussan.

This work was supported by the Science College Research Center at Qassim University, project No. SR-D-010-092.

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Al-Hussein, A. Necessary Conditions for Optimal Control of Stochastic Evolution Equations in Hilbert Spaces. Appl Math Optim 63, 385–400 (2011). https://doi.org/10.1007/s00245-010-9125-6

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  • DOI: https://doi.org/10.1007/s00245-010-9125-6

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