Approximate Controllability for a Semilinear Stochastic Evolution System with Infinite Delay in L_p Space

In this paper, approximate controllability for a class of infinite-delayed semilinear stochastic systems in L_p space (2 < p< ∞) is studied. The fundamental solution’s theory is used to describe the mild solution which is obtained by using the Banach fixed point theorem. In this way the approximate controllability result is then obtained by assuming that the corresponding deterministic linear system is approximately controllable via the so-called the resolvent condition. An application to a Volterra stochastic equation is also provided to illustrate the obtained results.