  This paper is concerned with the Fokker-Planck (FP) description of classical
stochastic systems with discrete time delay. The non-Markovian character of the
corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy
of FP equations for the various $n$-time joint distribution functions. Here we
present a novel approach to close the hierarchy at the one-time level based on
a linearization of the deterministic forces in all members of the hierarchy
starting from the second one. This leads to a closed equation for the one-time
probability density in the steady state. Considering two generic nonlinear
systems, a colloidal particle in a sinusoidal or bistable potential
supplemented by a linear delay force, we demonstrate that our approach yields a
very accurate representation of the density as compared to quasi-exact
numerical results from direct solution of the Langevin equation. Moreover, the
results are significantly improved against those from a small-delay
approximation and a perturbation-theoretical approach. We also discuss the
possibility of accessing transport-related quantities, such as escape times,
based on an additional Kramers approximation. Our approach applies to a wide
class of models with nonlinear deterministic forces.
