  The question of existence and properties of stationary solutions to Langevin
equations driven by noise processes with stationary increments is discussed,
with particular focus on noise processes of pseudo-moving-average type. On
account of the Wold-Karhunen decomposition theorem, such solutions are, in
principle, representable as a moving average (plus a drift-like term) but the
kernel in the moving average is generally not available in explicit form. A
class of cases is determined where an explicit expression of the kernel can be
given, and this is used to obtain information on the asymptotic behavior of the
associated autocorrelation functions, both for small and large lags.
Applications to Gaussian- and L\'{e}vy-driven fractional Ornstein-Uhlenbeck
processes are presented. A Fubini theorem for L\'{e}vy bases is established as
an element in the derivations.
