Abstract:
The aim of this work is to investigate a class of stochastic functional integrodifferential equations(SFIDEs) in a Hilbert space. We first study the existence of mild solutions of these equations by means of stochastic analysis theory and theory of resolvent operator in the sense of Grimmer. Further, the existence of optimal pairs for the corresponding Lagrange control systems is investigated.
Finally, an example is presented to illustrate our obtained results.
Description:
In the last decades stochastic differential equations have attracted considerable attention. These equations have been studied extensively since they are abstract formulations for many problems arising from economics, finance, physics, mechanics, electricity and control engineering, etc. (see [10, 15, 25]). There is much current interest in studying qualitative properties for SPDEs (see, e.g., [1, 2, 5, 26, 27]). In recent years, much attention has been paid to the qualitative properties of mild solutions to various stochastic integrodifferential equations by using the resolvent operator theory for integral equations and the fixed point technique see e.g., [14, 20, 28] and the references therein.
