[EN]In the framework known as stochastic inflation, the evolution of cosmological perturbations picks up a noise term. In this article we focus on the fact that in realistic applications of the model, the noise is actually coloured, which leads to memory
effects of modes of different scales. We evaluate the two- and three-point correlation function for the simple toy model of a scalar field with cubic self-interactions in a fixed de Sitter background. We show that in the presence of coloured noise perturbations of observable scale preserve some memory of the super-horizon modes, as scale-dependent imprints in their statistical moments. In particular, we find a blue tilt of the power-spectrum on large scales, and an enhancement of intrinsic non-Gaussianity.
