Controllability of stochastic semilinear systems

Abstract In this paper, we demonstrate that the exact controllability concept is inappropriate for stochastic systems by proving the nonfulfillment of the coercivity inequality. As a result, we explore the concept of C -controllability, which was introduced as a weaker alternative to exact controllability when the controllability problem was first extended to stochastic systems. We establish a sufficient condition for C -controllability in finite-dimensional semilinear stochastic systems driven by a Wiener process and illustrate the result with several examples.