Optimal controls problems for some impulsive stochastic integro-differential equations with state-dependent delay

In this paper, optimal control problems for a class of stochastic functional integral-differential equations in Hilbert spaces are investigated. First, the existence of mild solutions is investigated using stochastic analysis theory, fixed point theorems, and Grimmer's resolvent operator theory. Following that, the existence requirements of optimal pairs of systems governed by stochastic partial integro-differential equations with infinite delay are discussed. The results are achieved by the use of a combination of Lipschitz and Caratheodory conditions. At the end of the paper, an illustration is supplied to help highlight the key findings.