FEEDBACK OPTIMAL CONTROL FOR STOCHASTIC VOLTERRA EQUATIONS WITH COMPLETELY MONOTONE KERNELS

摘要

In this paper we are concerned with a class of stochastic Volterra integro-differential problems with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We start by reformulating the state equation into a semilinear evolution equation which can be treated by semigroup methods. The application to optimal control provides other interesting results and requires a precise description of the properties of the generated semigroup.