Necessary conditions of optimality for some stochastic integrodifferential equations of neutral type on Hilbert spaces
The authors consider partially observed control problems governed by stochastic integrodifferential equations of neutral type on Hilbert spaces driven by relaxed controls. Under some conditions, the existence and the uniquenes of mild solution which has a continuous modification are established. The continuity of the map \(u \mapsto x\), that is, the control to the solution map (endowed with certain weak topology) is proved. The authors also consider an optimal control problem of Bolza type. Using the above results they give necessary conditions of optimality for a class of stochastic integrodifferential equations of neutral type on Hilbert spaces. An example is given to illustrate the results.
scientific article; zbMATH DE number 6877185
scientific article