Abstract
In this chapter, we are concerned with the controllability problem for the simplest stochastic linear evolution equations, i.e., stochastic linear differential equations (with constant coefficients) in finite dimensions. A Kalman-type rank condition to characterize the exact controllability is given for the special case that the control matrix in the diffusion term is of full rank. Nevertheless, generally speaking, the controllability of stochastic linear differential equations in finite dimensions is surprisingly different from its deterministic counterpart.
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