[EN]We extend the formalism of stochastic inflation, with non-Markovian coloured noise, to describe the gauge-invariant
comoving curvature perturbation. We compute the power-spectrum of perturbations in this framework, after constraining the coarse-grained field to vanish when our local patch exited the Hubble radius, in order to remove the unobservable monopole. We find a blue tilt of the power-spectrum on the largest observable scales, in agreement with CMB data, which show a suppression of the low multipoles of the anisotropy. Our explanation of the anomalous behaviour of the lower multipoles of the CMB anisotropies does not require any ad-hoc new physical ingredients in the theory.
