  The stabilization by noise for parabolic equations in perforated domains,
i.e. domains with small holes, is investigated. We show that when the holes are
small enough, one can stabilize the unstable equations using suitable
multiplicative It\^o noise. The results are quantitative, in the sense that we
can explicitly estimate the size of the holes and diffusion coefficients for
which stabilization by noise takes place. This is done by using the asymptotic
behaviour of the first eigenvalue of the Laplacian as the hole shrinks to a
point.
