Complete controllability of semi-linear stochastic system with delay

This paper deals with the complete controllability of semilinear stochastic system with delay under the assumption that the corresponding linear system is completely controllable. The control function for this system is suitably constructed by using the controllability operator. With this control function, the sufficient conditions for the complete controllability of the proposed problem in finite dimensional are established. The results are obtained by using Banach fixed point theorem. Finally, one example is provided to illustrate the application of the obtained results.

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