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Applied Mathematics & Optimization

, Volume 63, Issue 3, pp 385–400 | Cite as

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

  • AbdulRahman Al-Hussein
Article

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.

Keywords

Martingale Stochastic evolution equation Stochastic maximum principle Optimal control Variational inequality Adjoint equation Backward stochastic partial differential equation 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceQassim UniversityBuraydahSaudi Arabia

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