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Unbounded perturbation of the controllability for stochastic evolution equations

Abstract:

In this paper we prove that the controllability for linear stochastic evolution equa- tions in Banach spaces is not destroyed if one perturbs the equation by "small" un- bounded linear operator. This is done by employing a perturbation principle from linear operator theory and a characterization of surjective operator in Banach spaces. Finally, we apply this result to a controlled system governed by the stochastic wave equation.