  It is well-known that the Manneville-Pomeau map with a parabolic fixed point
of the form $x\mapsto x+x^{1+\alpha} \mod 1$ is stochastically stable for
$\alpha\ge 1$ and the limiting measure is the Dirac measure at the fixed point.
In this paper we show that if $\alpha\in (0,1)$ then it is also stochastically
stable. Indeed, the stationary measure of the random map converges strongly to
the absolutely continuous invariant measure for the deterministic system as the
noise tends to zero.
