  The perturbative approach to stochastic inflation is used to determine the
spectrum of density fluctuations and gravitational waves due to the coarse
grained field. The amplitude of the curvature fluctuation spectrum, the
spectral index and the running of the spectral index are in general found to be
smaller than in the standard approach to inflation. Furthermore, the amount of
non-gaussianity due to the second order perturbation is estimated.
