  We extend investigations of infrared dynamics in accelerating universes. In
the presence of massless and minimally coupled scalar fields, physical
quantities may acquire growing time dependences through quantum fluctuations at
super-horizon scales. From a semiclassical viewpoint, it was proposed that such
infrared effects are described by a Langevin equation. In de Sitter space, the
stochastic approach has been proved to be equivalent to resummation of the
growing time dependences at the leading power. In this paper, we make the
resummation derivation of the Langevin equation in a general accelerating
universe. We first consider an accelerating universe whose slow-roll parameter
is constant, and then extend the background as the slow-roll parameter becomes
time dependent. The resulting Langevin equation contains a white noise term and
the coefficient of each term is modified by the slow-roll parameter.
Furthermore we find that the semiclassical description of the scalar fields
leads to the same stochastic equation as far as we adopt an appropriate time
coordinate.
