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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 469390, 9 pages
http://dx.doi.org/10.1155/2013/469390
Research Article

Necessary Conditions for Optimality for Stochastic Evolution Equations

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

Received 2 May 2013; Accepted 14 August 2013

Academic Editor: Fuding Xie

Copyright © 2013 AbdulRahman Al-Hussein. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with providing the maximum principle for a control problem governed by a stochastic evolution system on a separable Hilbert space. In particular, necessary conditions for optimality for this stochastic optimal control problem are derived by using the adjoint backward stochastic evolution equation. Moreover, all coefficients appearing in this system are allowed to depend on the control variable. We achieve our results through the semigroup approach.