  Stochastic description of inflationary spacetimes emulates the growth of
vacuum fluctuations by an effective stochastic ``noise field'' which drives the
dynamics of the volume-smoothed inflaton. We investigate statistical properties
of this field and find its correlator to be a function of distance measured in
units of the smoothing length. Our results apply for a wide class of smoothing
window functions and are different from previous calculations by Starobinsky
and others who used a sharp momentum cutoff. We also discuss the applicability
of some approximate noise descriptions to simulations of stochastic inflation.
