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Complete controllability of stochastic evolution equations with jumps. (English) Zbl 1244.93028
Summary: 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.
MSC:
93B05Controllability
60H15Stochastic partial differential equations
60J75Jump processes
93E03General theory of stochastic systems
93C25Control systems in abstract spaces