Can all the infrared secular growth really be understood as increase of
  classical statistical variance?
  It is known that in the theory of light scalar fields during inflation,
correlation functions suffer from infrared (IR) divergences or large IR loop
corrections, leading to the breakdown of perturbation theory. In order to
understand the physical meaning of such IR enhancement, we investigate the
stochastic properties of an effective equation of motion (EoM) for
long-wavelength modes of a canonically normalized light scalar field $\phi$
with a general sufficiently flat interaction potential on de Sitter background.
Firstly, we provide an alternative refined derivation of the effective action
for long-wavelength modes which leads to the effective EoM that correctly
reproduces all the IR correlation functions in a good approximation at a late
time, by integrating out short-wavelength modes. Next, under the assumption
that one can neglect non-local correlations in the influence functional
exceeding the coarse-graining scale, we show that the effective EoM for IR
modes of the "average field" in Schwinger-Keldysh formalism $\phi^<_c$ can be
interpreted as a classical stochastic process in the present model.
