  We develop a Lagrangian approach based on the influence functional method so
as to derive self-consistently the Langevin equation for the inflaton field in
the presence of trapping points along the inflaton trajectory. The Langevin
equation exhibits the backreaction and the fluctuation-dissipation relation of
the trapping. The fluctuation is induced by a multiplicative colored noise that
can be identified as the the particle number density fluctuations and the
dissipation is a new effect that may play a role in the trapping with a strong
coupling. In the weak coupling regime, we calculate the power spectrum of the
noise-driven inflaton fluctuations for a single trapping point and studied its
variation with the trapping location. We also consider a case with closely
spaced trapping points and find that the resulting power spectrum is blue.
