Stochastic Effects in Anisotropic Inflation
  We revisit the stochastic effects in the model of anisotropic inflation
containing a $U(1)$ gauge field. We obtain the Langevin equations for the
inflaton and gauge fields perturbations and solve them analytically. We show
that if the initial value of the electric field is larger than its classical
attractor value, then the random stochastic forces associated with the gauge
field is balanced by the frictional damping (classical) force and the electric
field falls into an equilibrium (stationary) regime. As a result, the classical
attractor value of the electric field is replaced by its stationary value. We
show that the probability of generating quadrupolar statistical anisotropy
consistent with CMB constraints can be significant.
