Applied Mathematics and Optimization, Vol.77, No.2, 343-375, 2018
Necessary Conditions of Optimality for Some Stochastic Integrodifferential Equations of Neutral Type on Hilbert Spaces
In this work, we develop the necessary conditions of optimality for partially observed control problems governed by stochastic integrodifferential equations of neutral type on Hilbert spaces driven by relaxed controls. Under suitable conditions, we establish the existence and the uniqueness of mild solution which has a continuous modification. We prove the continuity of the control to the solution map. Then we consider an optimal control problem of Bolza type. Using these results we give necessary conditions of optimality for a class of stochastic integrodifferential equations of neutral type on Hilbert spaces.
Keywords:Integrodifferential equations;Neutral type;Resolvent operator;Mild solutions;Hilbert spaces;Relaxed controls;Optimal control;Necessary conditions