A new algorithm for calculating the curvature perturbations in
  stochastic inflation
  We propose a new approach for calculating the curvature perturbations
produced during inflation in the stochastic formalism. In our formalism, the
fluctuations of the e-foldings are directly calculated without perturbatively
expanding the inflaton field and they are connected to the curvature
perturbations by the $\delta N$ formalism. The result automatically includes
the contributions of the higher order perturbations because we solve the
equation of motion non-perturbatively. In this paper, we analytically prove
that our result (the power spectrum and the nonlinearity parameter) is
consistent with the standard result in single field slow-roll inflation. We
also describe the algorithm for numerical calculations of the curvature
perturbations in more general inflation models.
