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The non-linear dynamics of long-wavelength cosmological fluctuations may bephrased in terms of an effective classical, but stochastic evolution equation.The stochastic noise represents short-wavelength modes that continuallyredshift into the long-wavelength domain. The effective evolution may bederived from first principles quantum field theory in an expanding background,through a sequence of approximations calling for additional scrutiny. Weperform such an analysis, putting particular emphasis on the amplitude of thestochastic noise, which ultimately determines the cosmological correlations andprovides a non-perturbative IR regulator to the dynamics.

Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude