Controllability of Linear Stochastic Systems in Hilbert Spaces

The classical theory of controllability for deterministic systems is extended to linear stochastic systems defined on infinite-dimensional Hilbert spaces. Three types of stochastic controllability are studied: approximate, complete, and S-controllability. Tests for complete, approximate, and S-controllabilities are proved and the relation between the controllability of linear stochastic systems and the controllability of the corresponding deterministic systems is studied