Approximate Controllability of Impulsive Stochastic Evolution Equations

Abstract

In this paper, we study the approximate controllability of nonlinear impulsive stochastic differential equations in a real separable Hilbert space. We prove the approximate controllability of nonlinear impulsive stochastic control systems under the assumption that the corresponding linear system is approximately controllable. By using the stochastic analysis theory and a fixed point strategy, sufficient conditions are formulated and proved. Moreover, an example is also provided to illustrate the effectiveness of the result.