Complete Controllability of Stochastic Evolution Equations with Jumps

The objective of this paper is to investigate the complete controllability property of a nonlinear stochastic control system with jumps in a separable Hilbert space. By employing a fixed point approach without imposing severe compactness condition on the semigroup, a new set of sufficient conditions are derived for achieving the required result. In particular, we discuss the complete controllability of nonlinear control system under the assumption that the corresponding linear system is completely controllable. Finally, an example is provided to illustrate the effectiveness of the obtained result.