Optimal control for a class of nonlinear stochastic hereditary systems (Q1262288)

Recently \textit{D. Reber} [J. Differ. Equations 68, 22-35 (1987; Zbl 0617.34072)] has introduced a function space for the study of nonlinear hereditary differential equations. This state space permits a satisfactory treatment of optimization problems under more general control functions. In the present paper we consider this space as the initial state space of the trajectories associated to nonlinear stochastic hereditary equations of Ito type. Existence, uniqueness, and continuous dependence results for such equations are obtained in Section 2. An optimization problem is considered in Section 3 and the existence of discrete \(\epsilon\)-optimal controls is proved.