  We adopt methods from statistical field theory to stochastic inflation. For
the example of a free test field in de Sitter and power-law inflation, the
power spectrum of long-wavelength fluctuations is computed. We study its
dependence on the shape of the filter that separates long from short wavelength
modes. While for filters with infinite support the phenomenon of dimensional
reductions is found on large super-horizon scales, filters with compact support
return a scale-invariant power spectrum in the infra-red. Features of the power
spectrum, induced by the filter, decay within a few e-foldings. Thus the
late-time power spectrum is independent of the filter details.
