  We consider the small deviation probabilities (SDP) for sums of stationary
Gaussian sequences. For the cases of constant boundaries and boundaries tending
to zero, we obtain quite general results. For the case of the boundaries
tending to infinity, we focus our attention on the discrete analogs of the
fractional Brownian motion (FBM). It turns out that the lower bounds for the
SDP can be transferred from the well studied FBM caseto the discrete time
setting under the usual assumptions that imply weak convergence while the
transfer of the corresponding upper bounds necessarily requires a deeper
knowledge of the spectral structure of the underlying stationary sequence.
