Stochastic non-attractor inflation
  We extend the formalism of stochastic inflation to the setup of non-attractor
inflation with a sound speed $c_s$. We obtain the Langevin equations for the
superhorizon perturbations and calculate the stochastic corrections to
curvature perturbation power spectrum. It is shown that the fractional
stochastic corrections in mean number of e-folds and power spectrum are at the
order of power spectrum. We also calculate the boundary crossing and the first
hitting probabilities in a hypothetical dS space with two boundaries in field
space. Furthermore, the stochastic corrections in power spectrum in a setup
akin to eternal inflation with large diffusion term are calculated.
