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The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noiseasymptotics for invariant densities for a class of diffusions: a controltheoretic view, J. Math. Anal. and Appl. (2009) " is flawed. We give here acorrected proof.

Small Noise Asymptotics for Invariant Densities for a Class of Diffusions: A Control Theoretic View (with Erratum)