Perturbations in stochastic inflation

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.