Abstract
One proves that the n-D stochastic controlled equation dX(t)+A(t)X(t)dt=σ(X(t))dW(t)+B(t)u(t)dt, where σ∈Lip(Rn,ℒ(Rd,Rn)), A(t)∈ℒ(Rn) and B(t)∈ℒ(Rn,Rn) is invertible, is exactly controllable with high probability in each y∈Rn such that σ(y)=0 on each finite interval (0,T). An application to approximate controllability of the stochastic heat equation is given. The case where B∈ℒ(Rm,Rn), 1≤m<n and the pair (A,B) satisfies the Kalman rank condition is also studied.
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