  We derive the non-equilibrium fluctuations of one-dimensional symmetric
simple exclusion processes in contact with slowed stochastic reservoirs which
are regulated by a factor $n^{-\theta}$. Depending on the range of $\theta$ we
obtain processes with various boundary conditions. Moreover, as a consequence
of the previous result we deduce the non-equilibrium stationary fluctuations by
using the matrix ansatz method which gives us information on the stationary
measure for the model. The main ingredient to prove these results is the
derivation of precise bounds on the two-point space-time correlation function,
which are a consequence of precise bounds on the transition probability of some
underlying random walks.
